Surface Areas and Volumes Test

Result

Surface Areas and Volumes Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

A solid right circular cone of base diameter 14 cm and height 8 cm is melted to form a hollow sphere. If the external diameter of the sphere is 10 cm, what is the internal diameter of the sphere?

A
3 cm

B
4 cm

C
6 cm

D
8 cm

Solution

The radius of the base of cone is 7 cm and the height is 8 cm.
Volume of the cone = (1/3)πr²h = (1/3) π (7)²x 8 cm³

External radius of the hollow sphere = 5 cm
Let the internal radius be r cm.

Volume of the hollow sphere = (4/3) π (R³- r³) cm³= (4/3) π (5³- r³) cm³

Since volume of material used for the cone will be same as the volume of material used to make the hollow sphere,

(1/3) π (7)² 8 = (4/3) π (125 - r³)
⇒ 98 = 125 - r³

r³= 125 - 98 = 27
r = 3 cm

So, internal diameter of the sphere = 2r = 2 x 3 = 6 cm
Question 2
1 / -0

A sphere with radius r is cut into two halves by a plane passing through the centre of the sphere. Two hemispheres of same radii are formed. Which of the following relations is true in this case?

A
Surface area of the sphere = Sum of the surface areas of the two hemispheres

B
Surface area of the sphere = Sum of the curved surface areas of the two hemispheres

C
Surface area of each hemisphere = Surface area of the sphere

D
Surface area of the sphere = Sum of the total surface areas of the two hemispheres

Solution

Surface area of sphere = 4πr²
And curved surface area of hemisphere = 2πr²

A sphere is cut into two hemispheres.

So, surface area of sphere = C.S.A of the I^st hemisphere + C.S.A of the
II^nd hemisphere

4πr² = 2πr² + 2πr²
4πr² = 4πr²

L.H.S = R.H.S