Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 11 Mensuration Questions Solution. In this chapter, there is total 35 math problems. We have given each questions solution step by step.
Edudel Class 8 Mental Maths Chapter 11 Mensuration:
Based on the given figures 1 and figure 2, answer the following questions from 1 to 4.
1.) Find the area and perimeter of the square.
ANSWER:
Given that,
Square of side 60m.
We know,
Area of square = (side) 2
Area of square = (60) 2
Area of square = 3600m2
Now,
Perimeter of Square = 4 x side
Perimeter of Square = 4 x 60
Perimeter of Square = 240m.
2.) Find the area and perimeter of the rectangle.
ANSWER:
Given that,
Rectangle of length 80 m and Breadth 30 m.
We know,
Area of rectangle = Length x Breadth
Area of rectangle = 80 x 30
Area of rectangle = 2400m2
Now,
Perimeter of rectangle = 2 x (Length + Breadth)
Perimeter of rectangle = 2 x (80 + 30)
Perimeter of rectangle = 220m.
3.) Which figure has less area and by how much?
ANSWER:
Area of square = 3600m2
Area of rectangle = 2400m2
Rectangle has less area.
3600m2 – 2400m2 = 1200 m2
Rectangle area is less by 1200 m2
4.) Whose perimeter is greater and by how much?
ANSWER:
Perimeter of Square = 240m.
Perimeter of rectangle = 220m.
From given data,
Perimeter of square is greater than rectangle.
240m – 220 m
Perimeter of square is greater by 20m.
5.) Find the area of the rhombus whose diagonals are 16cm and 12cm.
ANSWER:
Given that,
Diagonals of rhombus are 16cm and 12cm.
We have to find area of the rhombus.
Area of the rhombus = 1/2 x Diagonal1 x Diagonal2
Area of the rhombus = 1/2 x 16cm x 12cm.
Area of the rhombus = 96 cm2
6.) Find the perimeter of the rhombus given in question 5.
ANSWER:
Given that,
Diagonals of rhombus are 16cm and 12cm.
We have to find perimeter of the rhombus.
We use right angled triangle theorem,
(Side of rhombus) 2 = 8 2 + 6 2
(Side of rhombus) 2 = 64 + 36
(Side of rhombus) 2 = 100
Side of rhombus = 10
Perimeter of rhombus = 4 x side
Perimeter of rhombus = 4 x 10
Perimeter of rhombus = 40m.
7.) If the radius of the circle is 14 cm, find the diameter of the circle.
ANSWER:
Given that,
Radius of the circle is 14 cm
We have to find diameter of the circle.
We know,
Diameter of the circle = 2 x radius
Diameter of the circle = 2 x 14
Diameter of the circle = 28 cm.
8.) Find the circumference of the circle whose diameter is 28 cm.
ANSWER:
Given that,
Diameter of the circle is 28 cm.
We have to find the circumference of the circle.
The circumference of the circle = π x Diameter
The circumference of the circle = 22/7 x 28 cm.
The circumference of the circle = 88 cm.
9.) Find the area of the circle of radius 7 cm.
ANSWER:
Given that,
Radius of the circle is 7 cm.
We have to find the area of the circle.
We know,
The area of the circle = π x (radius) 2
The area of the circle = 22/7 x (7) 2
The area of the circle = 22 x 7
The area of the circle = 154 cm2
10.) In the given figure, the breadth of the rectangle is 3 m and the length of diagonal is 5 m. find the perimeter of the rectangle.
ANSWER:
Given that,
The breadth of the rectangle is 3 m and the length of diagonal is 5 m.
Here we use Pythagoras theorem,
52 = 32 + (Length of rectangle) 2
(Length of rectangle) 2 = 25 – 9
(Length of rectangle) 2 = 16
(Length of rectangle) = 4
Perimeter of rectangle = 2 x (Length + Breadth)
Perimeter of rectangle = 2 x (4 + 3)
Perimeter of rectangle = 14 m.
11.) Find the area of the rectangle given in question 10.
ANSWER:
Length of rectangle = 4m.
Breadth of the rectangle = 3 m
Area of rectangle = Length x Breadth
Area of rectangle = 4 x 3
Area of rectangle = 12m2
12.) If the side of a cube is 4 cm. Find its lateral surface area.
ANSWER:
Given that,
Side of a cube is 4 cm
We have to find lateral surface area.
We know,
Lateral surface area of cube = 4 x (side) 2
Lateral surface area of cube = 4 x (4) 2
Lateral surface area of cube = 4 x 16
Lateral surface area of cube = 64 cm2
13.) Find the total surface area of a cube of side 6 cm.
ANSWER:
Given that,
Side of a cube is 6 cm
We have to find total surface area of a cube.
We know,
Total surface area of a cube = 6 x (side) 2
Total surface area of a cube = 6 x (6) 2
Total surface area of a cube = 6 x 36
Total surface area of a cube = 216 cm2
14.) If the diameters of two circles are 14 cm and 7 cm, find the ratio of their areas.
ANSWER:
Given,
The diameters of two circles are 14 cm and 7 cm.
We have to find ratio of their areas.
We know,
The area of the circle = π x (radius) 2
The area of the circle = π x (Diameter/2) 2
Ratio of areas of 2 circles = (Diameter1/2) 2 / (Diameter2/2) 2
Ratio of areas of 2 circles = 72 / 3.52
Ratio of areas of 2 circles = 49 / 12.25
Ratio of areas of 2 circles = 4:1
15.) The height of a cylinder is 14 cm and its radius is 7 cm. Find the total surface area of the cylinder.
ANSWER:
Given that,
The height of a cylinder is 14 cm and its radius is 7 cm
We have to find total surface area of the cylinder.
We know,
Total surface area of the cylinder = 2πr x (h + r)
Where h= height and r = radius.
Total surface area of the cylinder = 2 x (22/7) x 7 x (14 + 7)
Total surface area of the cylinder = 44 x 21
Total surface area of the cylinder = 924 sq. cm
16.) Find the volume of the cylinder given in question 15.
ANSWER:
Given that,
The height of a cylinder is 14 cm and its radius is 7 cm
We have to find the volume of the cylinder.
We know,
The volume of the cylinder = π x (radius)2 x h
The volume of the cylinder = (22/7) x 49 x 14
The volume of the cylinder = 22 x 7 x 14
The volume of the cylinder = 2156 cm3
17.) Find the side of the cube whose total surface area is 9600 sq. m.
ANSWER:
Given that,
Total surface area of cube is 9600 sq. m.
We have to find the side of the cube.
We know,
Total surface area of a cube = 6 x (side) 2
9600 sq. m. = 6 x (side) 2
(Side) 2 = 9600 sq. m. / 6
(Side) 2 = 1600
Side = 40 m
The side of the cube is 40m.
18.) Find the volume of the cube given in question 17.
ANSWER:
The side of the cube is 40m.
We have to find the volume of the cube.
We know,
The volume of the cube = (side) 3
The volume of the cube = 403
The volume of the cube = 64000 m3
19.) Find the total surface area of the cuboid as shown in the figure.
ANSWER:
From figure,
Length of cuboid (l) = 6m.
Width of cuboid (b) = 3m
Height of cuboid (h) = 5m
We know,
Total surface area of the cuboid = 2 x (lb + bh +hl)
Total surface area of the cuboid = 2 x ((6 x 3) + (3 x 5) + (6 x 5))
Total surface area of the cuboid = 2 x (18 + 15 + 30)
Total surface area of the cuboid = 2 x 63
Total surface area of the cuboid = 126 m2
20.) Find the volume of the cuboid given in question 19.
ANSWER:
From figure,
Length of cuboid (l) = 6m.
Width of cuboid (b) = 3m
Height of cuboid (h) = 5m
We know,
The volume of the cuboid = Length x Width x Height
The volume of the cuboid = 6 x 3 x 5
The volume of the cuboid = 90 m3
21.) Find the height of the cuboid whose base area and volume are 800 square meter and 6400 cubic meter respectively.
ANSWER:
Given,
Base area of the cuboid = 800 square meter
Volume of the cuboid = 6400 cubic meter
We have to find the height of the cuboid.
We know,
Base area of the cuboid = Length x Width
Length x Width = 800 square meter
Now,
We know,
The volume of the cuboid = Length x Width x Height
The volume of the cuboid = 800x Height
The height of the cuboid = 6400 cubic meter / 800
The height of the cuboid = 8m.
- ) A cuboid is of dimensions 50 cm x 40 cm x 30 cm. How many small cubes each having side of 10cm can be placed in the given cuboid?
ANSWER:
Given,
A cuboid is of dimensions 50 cm x 40 cm x 30 cm.
We have to find no. of small cubes each having side of 10cm.
No. of small cubes each having side of 10cm = Volume of cuboid/ Volume of cube
No. of small cubes each having side of 10cm = 50 cm x 40 cm x 30 cm / 10 x 10 x 10
No. of small cubes each having side of 10cm = 60000 / 1000
No. of small cubes each having side of 10cm = 60
23.) A cuboidal tank is 8 m long, 6 m wide and 2 m deep. How many litres of water it can hold?
ANSWER:
Given that,
A cuboidal tank is 8 m long, 6 m wide and 2 m deep.
We have to find how many litres of water it can hold.
We know,
The volume of the cuboid = Length x Width x Height
The volume of the cuboid = 8 m x 6 m x 2 m
The volume of the cuboid = 96 m3
We know,
1m3 = 1000 litre
96 m3 = 96 x 1000 litre
96000 litreswater it can hold.
24.) Volume of a cube is 3375 cubic cm. What is the length of the side of the cube?
ANSWER:
Given that,
Volume of a cube is 3375 cubic cm.
We have to find length of the side of the cube
We know,
Volume of a cube = (side) 3
3375 = (side) 3
Side = 15 cm
length of the side of the cube is 15 cm.
25.) Find the area of the given figure.
ANSWER:
We have to find area of given figure.
We make some changes in given figure.
We make combination of Rectangle and Triangle.
Area of Rectangle = Length x Breadth
Area of Rectangle = 13 x 10
Area of Rectangle = 130 cm2
Area of triangle = 1/2 x base x height
Area of triangle = 1/2 x 10 x 7
Area of triangle = 35 cm2
Area of given figure = Area of rectangle + Area of Triangle
Area of given figure =130 cm2 + 35 cm2
Area of given figure =165 cm2
26.) The sides of a room are in the ratio 3:2:4 The volume of the room is 24000 cubic meter. Find the length of the longest side of the room.
ANSWER:
Given,
The sides of a room are in the ratio 3:2:4
The volume of the room is 24000 cubic meter.
Let, sides of a room are 3x, 2x and 4x.
We know,
The volume of the cuboid room= Length x Width x Height
The volume of the cuboid room =3x X 2x X 4x.
24000 = 24x3
x3 = 24000 / 24
x3 = 1000
x = 10
The length of the longest side of the room is 4x = 4 x 10 = 40 m
27.) Find the area of shaded portion
ANSWER:
We have to find, area of shaded portion
Area of inner rectangle = Length x Breadth
Area of inner rectangle = 10 x 5
Area of inner rectangle = 50 cm2
Area of outer rectangle = Length x Breadth
Area of outer rectangle = 30 x 15
Area of outer rectangle = 450 cm2
Area of shaded portion = Area of outer rectangle – Area of inner rectangle
Area of shaded portion =450 cm2 – 50 cm2
Area of shaded portion = 400 cm2
28.) As shown in the given figure, two concentric circles having centre O, OA = 14 cm and OB = 7 cm. Find the area of the shaded portion.
ANSWER:
We have to find area of the shaded portion.
Area of inner circle = π x (radius) 2
Area of inner circle = 22/7 x 49
Area of inner circle = 154 cm2
Area of outer circle = π x (radius) 2
Area of outer circle =22/7 x 196
Area of outer circle = 22 x 28
Area of outer circle = 616 cm2
Area of shaded portion =616 cm2 – 154 cm2
Area of shaded portion =462cm2
29.) As shown in the given figure, AC = 15 cm, DQ = 8 cm, BP = 10 cm. Find the area of the figure.
ANSWER:
We know,
Area of triangle1 = 1/2 x base x height
Area of triangle1 = 1/2 x 15 x 8
Area of triangle1 = 60cm2
Area of triangle2 = 1/2 x base x height
Area of triangle2 = 1/2 x 15 x 10
Area of triangle2 = 75 cm2
Area of given figure = Area of triangle1+ Area of triangle2
Area of given figure =60cm2 + 75 cm2
Area of given figure = 135 cm2
30.) If the radius of circle is doubled, then by how much percent its area will increase?
ANSWER:
Given that,
Radius of circle is doubled.
We know,
Area of circle = π x (radius) 2
Area of circle is directly proportional to (radius) 2
Area of circle = (2 x radius) 2
Area of circle is increase by 400%
31.) The area of four walls of a room is 48 sq.m. If perimeter of the floor is 16m, find the height of the room.
ANSWER:
Given,
The area of four walls of a room is 48 sq.m.
Perimeter of the floor is 16m
We have to find the height of the room.
The height of the room = the area of four walls / Perimeter of the floor
The height of the room = 48 / 16
The height of the room = 3 m.
32.) Find the area of a trapezium shaped field whose parallel sides are 132.7m and 67.3m respectively and distance between parallel sides is 23.75m.
ANSWER:
Given that,
Parallel sides of trapezium are 132.7m and 67.3m respectively and distance between parallel sides is 23.75m.
We have to find the area of a trapezium.
The area of a trapezium = 1/2 x (a + b) x h
a and b are parallel sides and h is distance between parallel sides
The area of a trapezium = 1/2 x (132.7m + 67.3m) x 23.75m
The area of a trapezium = 1/2 x 200 x 23.75m
The area of a trapezium = 2375 m2
33.) The capacity of a cylindrical tank, whose base diameter is 4m is 44000 litres. Find its height.
ANSWER:
Given,
The capacity of a cylindrical tank, whose base diameter is 4m is 44000 litres
We have to find height of cylindrical tank.
We know,
Volume of cylindrical tank = π x (radius) 2 x h
44 = 22/7 x (2)2 x h
h = 44 x 7 / 22 x 4
h =3.5m
34.) If the radius of a cylindrical tank is reduced to half of original radius, then what will be the change in its height if the volume of the cylinder remains same?
ANSWER:
If the radius of a cylindrical tank is reduced to half of original radius, then the change in its height if the volume of the cylinder remains same is 4 times.
35.) The area of the circular base of a cylindrical tank is 220sq.cm. Find its volume if its height is 40cm.
ANSWER:
Given,
The area of the circular base of a cylindrical tank is 220sq.cm
Height of a cylindrical tank = 40cm.
We have to find volume of a cylindrical tank.
We know,
Volume of cylindrical tank = height x circular base of a cylindrical tank
Volume of cylindrical tank = 40 x 220sq.cm
Volume of cylindrical tank =8800 cm3
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