Telangana SCERT Solution Class X (10) Maths Chapter 10 Mensuration Exercise 10.1
Exercise 10
1) A jokers cap in the form of right circular cone whose base radius is 7cm and height is 24cm. Find the area of the sheet required to make 10 such caps,
Ans:
Given that, Right circular con’s (Joker cap)
Height h=24cm
Radius r = 7cm
Area of the cone (Joker cap)
= π r l
= 22/7 x 7 (√h2 + r2)
= 22/7 x 7 x (√(24)2+(7)2)
= 22 x √576+49
= 22 x √625
= 22 x 25
= 550cm2
Therefore, Area of one Joker cap = 550cm2
The Area of the Sheet required make 10 caps = 550 x 10
= 5500 cm2
2) A sports company was ordered to prepare 100 paper cylinders for making packing shuttle cooks. The required dimensions of the cylinders are 35 cm length/height and its radius is 7cm. Find the required area of thick paper sheet needed to make 100 cylinders.
Ans:
Given That, Paper cylinders
Radius r= 7cm
height h= 35cm
Curve surface Area of the Paper Cylinders = 2 π rh
= 2 x 22/7 x 7 x 35
= 1540 cm2
Total sheet required to make 100 paper cylinders
= 1540 x 100
= 154000 cm2
= 154000/10000
= 15.4 m2
3) Find the Volume of right circular cone with radius 6cm and height 7 cm
Ans:
Given that, Right circular cones
Radius r = 6cm
height h = 7 cm
Volume V = 1/3 π r2 h
= 1/3 x 22/7 x 6 x 6 x 7
= 264 cm3
Therefore, The volume of right circular Cone = 264 cm3
4) The lateral surface area of a cylinder is equal to the curved surface area of a cone. if their bases are the same, find the ratio of the height of the cylinder to the sight height of the cone.
Ans:
Given that, Radius of the cylinder = radius
Curve surface area of the cylinder curve surface area of the cone
2 π r h = π r l
2h = l
h/l = ½
H:l = 1:2
Therefore the ratio of the height of Cylinder to the slant height of the cone is 1:2
5) A self help group wants to manufacture jokers caps of 3 cm radius and 4cm height. if the available paper sheet is 1000cm2 , then how many caps can be manufactured from that paper sheet ?
Ans:
Given that, conical joker caps
radius r = 3 cm
Height h = 4cm
Slant height l = √h2 + r2
= √42 + 32
l = √16 + 9
l = √25
l = 5cm
Curve surface area of the joker cap
= π r l
= 22/7 x 3 x 5
= 330 / 7cm2
Total area of available colour paper = 1000 cm2
Therefore, Number of caps can be made from 1000cm2 Colour paper = 1000/330/7
= 1000 x 7/330
= 700/33
= 21 caps
Therefore, 21 caps are manufactured from paper sheet.
6) A cylinders and cone have bases of equal radii and area of equal heights. Show that their volumes are in the ratio of 3:1
Ans:
Let the radius of the cylinders = radius of the cone = r
The height of the cylinder = height of cone = h
The ratio of the volume of cylinder and cone
= π r2 h = 1/3 π r2 h
= 1 = 1/3
= 3:1
Hence proved
7) The Shape of solid iron is cylindrical, its height is 11 cm and base diameter is 7 cm. Then find the total volume of 50 such rods.
Ans:
Given that, Cylindrical shaped rods
Diameter d = 7 cm
Radius r = 7/2 cm
Height h = 11 cm
Therefore, Volume of the rod = π r2 h
= 22/7 x 7/2 x7/2 x 11
= 11 x 11 x 7/2
= 847/ 2
= 423.5 cm3
Therefore, Volume of 50 rods
= 423.5 x 50
= 21175.0
= 21175 cm3
Therefore, Volume of 50 rod = 211753
8) A heap of rice is in the form of cone of Diameter 12m and height 8 cm. Find its volume. How much canvas cloth is required to cover the heap.
Ans:
Given that, heap of rice in the form of Cone
Diameter d = 12m
radius r = d/2
= 12/2
r = 6m
Height h = 8m
Volume of the rice = 1/3 π r2 h
= 1/3 x 3.14 x 6 x 6 x 8
= 3.14 x 6 x 8 x 2
= 3.14 x 96
= 301.44m3
Short Height,
l = √h2+r2
= √ 82 + 62
= √64+36
= √100
l= 10m
Curve surface area of the cone = π r l
= 3.14 x 6 x 10
= 188.40
= 188.4m2
Therefore, the area of the canvas cloth required to Cover the heap = 188.4 m2
9) The Curved surface area of a cone is 4070 cm2 and its diameter is 70 cm. what is its slant height.
Ans:
given that = Cones diameter d ‘= 70 cm
Radius r = d/2
= 70/2
= 35 cm
Curve surface area of the cone = 4070 cm2
=> π r l = 4070
=> 22/7 x 3.5 x l = 4070
l = 4070 x 22/7 x 1/35
l = 370 x 7/2 x 1/35
=> 370 x ½ x 1/5
=>370/10
=> 37 cm
Therefore, Slant height of the Cone = 37 cm
Here is your solution of Telangana SCERT Class 10 Math Chapter 10 Mensuration Exercise 10.1
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