Telangana SCERT Solution Class X (10) Maths Chapter 10 Mensuration Exercise 10.2
1) A toy is in the form of a mounted on a hemisphere of the same diameter. The diameter of the base and the height of the cone are 6cm and 4cm respectively. Determine the surface area of the toy. π
Ans:
Given Cones, Diameter d = 6CM
Radius r = d/2
= 6/2
= 3
Height h = 4cm
Slant height l = √h2+r2
= √42+ 32
= √16+9
= √25
l = 5
Curve surface area of the cone = π r l
= 3.14 x 3 x 5
= 47.10
= 47.1cm2
Given hemisphere radius r = 3cm
Curve surface area of hemisphere
= 2 π r2
= 2 x 3.14 x 3 x 3
= 56.52 cm2
Therefore, surface area of the toy = Curve surface area of the cone + curve surface area of the hemisphere
= 47.1 cm2 + 56.52 cm2
= 103.62 cm2
therefore surface area of the given toy is 103.62 cm2
2) A solid is in the form of a right circular cylinder with the hemisphere at one end and a cone at the other end the radius of the common base is 8 cm and the height of the cylindrical and conical portions are 10 cm and 6 CM respectively find the total surface area of the solid
Given cones radius r = 8 cm
Height h = 6cm
Slant Height
l = √h2 + r2
= √62 + 82
= √36 + 81
= √100
l = 10 cm
Curve Surface Area = π r l
= 3.14 x 8 x 10
= 3.14 x 80 cm2
Cylinders of Radius (r) = 8cm
Height h = 10 cm
Curve Surface Area = 2 π r h
= 2 x 3.14 x 8 x 10
= 3.14 x 160 cm2
Hemisphere of Radius (r) = 8cm
Curve surface area = 2 π r2
= 2 x 3.14 x 8 x 8
= 3.14 x 128 cm2
Total surface area of the solid = C.S.A of the Cone + C.S.A Cylinder + C.S.A of Hemisphere
= 3.14 x 80 x 3.14 x 160 x 3.14 x 128
= 3.14 x (80 + 160 + 128)
= 3.14 x 368
= 1155.52 cm2
Therefore, Total surface Area of solid is 1155.52 cm2
3) Medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends length of the capsule is 14 mm and the thickness is 5 mm. find its surface area.
Ans:
Cylinder Portions Diameter = 5mm
Radius = d/2 = 5/2 = 2.5 mm
= 14 – 5
= 9mm
Curved Surface Area = 2 π r h
= 2 x π x 2.5 x 9
= 45 π
Hemispherical Portions,
Radius = 2.5 mm
Curve Surface Area = 2 x π x 2.5 x 2.5
= 12.5 π
Now, Total Surface area of the Capsule = C.S.A of the cylinder + 2 x C.S.A of hemisphere
= 45 π + 2 x 12.5 π
= 70 π
= 70 x 3.14
= 70 x 3.14
= 70 x 22/7
= 10 x 22
= 220 mm2
4) Two cubes each of the volume 64cm3 are joined end to end together. Find the surface area of the resulting cuboid
Ans:
Let the Side of the cube be A
Volume of the Cube = 64cm3
a3 = 64cm3
a3 = 43
a = 4cm
Two Cubes of the sides 4cm joined end to end and form a cuboid
therefore, restaurant cuboid,
length l = 4+4 = 8cm
breadth = 4cm
height h = 4cm
Curve Surface Area of Cuboid = 2 (lb + bh + hl)
= 2 (8 x 4 + 4 x 4 + 4 x 8 )
= 2 (32 + 16 + 32)
= 2 (80)
= 160 cm2
Therefore surface area of the Cuboid is 160 cm2
5) A Storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of cylinder be 1.4 M and its length be 8m then find the cost of painting it on the outside at rate of is 120 per metre square
Ans:
given Cylindrical portions diameter = 1.4m
Radius r = d/2 = 1.4/2
= 0.7 m
height h= 8m
curve surface area = 2 π r h
= 2 x 22/7 x 0.7 x 8
= 352/2
= 35.2 cm2
Hemispherical Portions
Diameter d = 1.4m
Radius r = 0.7m
Curve Surface Area = 2 π r2
= 2 x 22/7 x 0.7 x 0.7
= 308 cm2
Total Surface area of a storage tank = CSA of Cylindrical Portion + CSA of 2 x Hemisphere Portion
= 35.2 cm2 + 2 x 3.08 cm2
= 41.36 cm2
therefore, cost of painting 1m2 = 20
41.36cm2 = 41.36 x 20
= 827.20
7) A hemisphere is cut out from one face of a cubical wooden block such that the diameter of the inner sphere is equal to side of the cube. Find the total surface area of the remaining solid.
Ans:
Let the Length of the cube be ‘a’
Total Surface area of the cube = 6a2
Hemisphere’s Radius = a/2
Curve surface area = 2 π r2
= 2 π (a/2)2
= 2 π x a2/4
= π a2/2
Area of the circle = π (a/2)2
= π a2/4
The Surface area of the remaining solid = total surface area of cube + curve surface area of Hemisphere – area of the Circle
= 6a2 + π a2/2 – π a2/4
= 6a2 + 2 π a2– π a2/4
= 6a2 + π a2/4
= a2 + (6+ π/4)
Therefore the surface area of the remaining solid is a2(6+ π/4)
8) A wooden article was made by scooping out a hemisphere from each end of the solid cylinder as shown in the figure if the height of the cylinder is 10 cm and its radius of the base is 3.5 CM find the total surface area of the article
Ans:
Given Wooden articles cylindrical portions radius r = 3.5 cm
height h = 10 cm
Curve surface area = 2 π r h
= 2 x 22/7 x 3.5 x 10
= 220 cm2
Hemispherical Portions radius = 3.5cm
Curve surface area = 2 π r2
2 x 22/7 x 3.5 x 3.5
= 77.0
= 77 cm2
Therefore surface area of the solid = CSA of cylinder + 2 x CSA of hemisphere
= 220 + 2x 77
= 220 + 154
= 374 cm2
Here is your solution of Telangana SCERT Class 10 Math Chapter 10 Mensuration Exercise 10.2
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