Mensuration Exercise15.4 – Questions
- Find the surface area of a sphere of radius 14 cm.
- Find the TSA of a hemisphere of radius 5 cm.
- 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.
- Calculate the surface area of the largest sphere that can be cut out of a cube of side 15 cm.
- Find the volume of the sphere whose radius is 7 cm.
- Find the volume of a sphere whose surface area is 154 cm2.
- The volume of a solid hemisphere is 1152πcm3. Find its curved surface area.
- 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?
- 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.
- 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
- 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
- Find the TSA of a hemisphere of radius 5 cm.
Solution:
TSA of hemisphere = 3πr2
= 3 x 22/7 x 52
= 235.71 cm2
- 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
- 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
- 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
- Find the volume of a sphere whose surface area is 154 cm2.
Solution:
We know, surface area of the sphere = 4πr2
154 = 4πr2
154/4π = 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
- 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 3/2π = r3
1728 = r3
r = 12 cm
CSA of hemisphere = 2πr2
= 2 x 22/7 x (12)2
= 905.14 cm2
- 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.
- 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
- 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