**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 cm**^{2}.**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 cm**^{2}.**The volume of a solid hemisphere is 1152πcm**^{3}. 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 = 4πr^{2}

= 4 x ^{22}/_{7} x 14^{2}

= 2464 cm^{2}

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

Solution:

TSA of hemisphere = 3πr^{2}

= 3 x ^{22}/_{7} x 5^{2}

= 235.71 cm^{2}

**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 cm**^{2}.

Solution:

diameter of the hemisphere = 10.5 cm

radius of the hemisphere = 5.25 cm

CSA of hemisphere = 2πr^{2}

= 2 x ^{22}/_{7} x 5.25^{2}

= 173.25 cm^{2}

The cost of painting it on the inside at the rate of Rs. 12 per 100 cm^{2}. Then the cost of painting the 173.25cm^{2} = ^{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 = 4πr^{2}

= 4 x ^{22}/_{7} x 7.5^{2}

= 707.14 cm^{2}

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

Solution:

Volume of the sphere = ^{4}/_{3 }πr^{3}

= ^{4}/_{3} x ^{22}/_{7} x 7^{3}

= 1437.33 cm^{3}

**Find the volume of a sphere whose surface area is 154 cm**^{2}.

Solution:

We know, surface area of the sphere = 4πr^{2}

154 = 4πr^{2}

^{154}/_{4π} = r^{2}

r^{2} = 12.54

r = 3.5 cm

Volume of the sphere = ^{4}/_{3 }πr^{3}

= ^{4}/_{3 }x ^{22}/_{7 }x 3.5^{3}

= 179.67 cm^{3}

**The volume of a solid hemisphere is 1152πcm**^{3}. Find its curved surface area.

Solution:

Volume of the hemisphere = ^{2}/_{3 }πr^{3}

1152π = ^{2}/_{3 }πr^{3}

^{1152π x 3}/_{2π} = r^{3}

1728 = r^{3}

r = 12 cm

CSA of hemisphere = 2πr^{2}

= 2 x ^{22}/_{7} x (12)^{2}

= 905.14 cm^{2}

**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}/_{3}πr^{3}

= ^{4}/_{3} x ^{22}/_{7} x (1.75)^{3}

= 25.45 mm^{3}

Therefore, 25.25mm^{3} 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 }πr_{s}^{3 }= ^{1}/_{3} πr_{c}^{2}h_{c}

^{4}/_{3 }πr_{s}^{3 }= ^{1}/_{3} π x 5^{2} x 20

4r_{s}^{3} = 5^{2} x 20

r_{s}^{3} = ^{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}/_{3}πr_{s}^{3} = πr_{w}^{2}h_{w}

^{4}/_{3}r_{s}^{3} = r_{w}^{2}h_{w}

^{4}/_{3} x 9^{3} = 0.2^{2}h_{w}

h_{w} = (^{4}/_{3} x 9^{3})/_{0.2}^{2}

h_{w }= 24300 cm

The length of the wire = 243 m