Tag: Mensuration Exercise 15.4 – class 10

Mensuration Exercise15.4 – Class 10 – Solutions

Mensuration Exercise15.4 – Questions

  1. Find the surface area of a sphere of radius 14 cm.
  2. Find the TSA of a hemisphere of radius 5 cm.
  3. A hemisphere bowl made of wood has inner diameter of 10.5 cm. Find the cost of painting it on the inside at the rate of Rs. 12 per 100 cm2.
  4. Calculate the surface area of the largest sphere that can be cut out of a cube of side 15 cm.
  5. Find the volume of the sphere whose radius is 7 cm.
  6. Find the volume of a sphere whose surface area is 154 cm2.
  7. The volume of a solid hemisphere is 1152πcm3. Find its curved surface area.
  8. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine is needed to fill this capsule?
  9. A right circular cone of height 20 cm and base radius 5 cm is melted and recast into a sphere. Find the radius of the sphere.
  10. The diameter of a metallic sphere is 18 cm. It is melted and drawn into a wire having diameter of cross section 0.4 cm. Find the length of the wire.

Mensuration Exercise15.4 – Solutions

  1. Find the surface area of a sphere of radius 14 cm.

Solution:

Surface area of the sphere = 4πr2

= 4 x 22/7 x 142

= 2464 cm2

 

  1. Find the TSA of a hemisphere of radius 5 cm.

Solution:

TSA of hemisphere = 3πr2

= 3 x 22/7 x 52

= 235.71 cm2

 

  1. A hemisphere bowl made of wood has inner diameter of 10.5 cm. Find the cost of painting it on the inside at the rate of Rs. 12 per 100 cm2.

Solution:

diameter of the hemisphere = 10.5 cm

radius of the hemisphere = 5.25 cm

CSA of hemisphere = 2πr2

= 2 x 22/7 x 5.252

= 173.25 cm2

The cost of painting it on the inside at the rate of Rs. 12 per 100 cm2. Then the cost of painting the 173.25cm2 = 173.25×12/100 = Rs. 20.79

 

  1. Calculate the surface area of the largest sphere that can be cut out of a cube of side 15 cm.

Solution:

d = 15 cm

r = d/2 = 15/2 = 7.5 cm

Surface area of the sphere = 4πr2

= 4 x 22/7 x 7.52

= 707.14 cm2

 

  1. Find the volume of the sphere whose radius is 7 cm.

Solution:

Volume of the sphere = 4/3 πr3

= 4/3 x 22/7 x 73

= 1437.33 cm3

 

  1. Find the volume of a sphere whose surface area is 154 cm2.

Solution:

We know, surface area of the sphere = 4πr2

154 = 4πr2

154/ = r2

r2 = 12.54

r = 3.5 cm

Volume of the sphere = 4/3 πr3

= 4/3 x 22/7 x 3.53

= 179.67 cm3

 

  1. The volume of a solid hemisphere is 1152πcm3. Find its curved surface area.

Solution:

Volume of the hemisphere = 2/3 πr3

1152π = 2/3 πr3

1152π x 3/ = r3

1728 = r3

r = 12 cm

CSA of hemisphere = 2πr2

= 2 x 22/7 x (12)2

=  905.14 cm2

 

  1. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine is needed to fill this capsule?

Solution:

d = 3.5 mm

r = d/2­ = 3.5/2 = 1.75 mm

Volume of the sphere = 4/3πr3

= 4/3 x 22/7 x (1.75)3

= 25.45 mm3

Therefore, 25.25mm3 medicine is needed to fill the capsule.

 

  1. A right circular cone of height 20 cm and base radius 5 cm is melted and recast into a sphere. Find the radius of the sphere.

Solution:

h = 20 cm

r = 5 cm

Volume of the sphere = Volume of the cone

4/3 πrs3 = 1/3 πrc2hc

4/3 πrs3 = 1/3 π x 52 x 20

4rs3 = 52 x 20

rs3 = 25×20/4 = 125

= 5 cm

 

  1. The diameter of a metallic sphere is 18 cm. It is melted and drawn into a wire having diameter of cross section 0.4 cm. Find the length of the wire.

Solution:

d = 18 cm

r = 9 cm

Volume of sphere = Volume of wire

4/3πrs3 = πrw2hw

4/3rs3 = rw2hw

4/3 x 93 = 0.22hw

hw = (4/3 x 93)/0.22

hw = 24300 cm

The length of the wire = 243 m