Question

30. A solid metallic sphere of radius 8 cm is melted to form 64 equal small solid spheres. The ratio of the surface area of this sphere to that of a small sphere is

Answer 1

Here is the answer.

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Answer 2

The ratio of the surface area of this sphere to that of a small sphere is 16 : 1

Step-by-step explanation:

Radius of big sphere = 8 cm

We are given that A solid metallic sphere of radius 8 cm is melted to form 64 equal small solid spheres.

Let R be the radius of one small sphere

Volume of big sphere = Volume of 64 small spheres

$(8)^3 = 64 \times R^3$

$\sqrt[3]{\frac{8^3}{64}}=R$

2 = R

Surface area of large sphere = $4 \pi r^2 = 4 \times \frac{22}{7} \times 8^2$

Surface area of small sphere =$4 \pi r^2 = 4 \times \frac{22}{7} \times 2^2$

The ratio of the surface area of this sphere to that of a small sphere =$\frac{4 \times \frac{22}{7} \times 8^2}{4 \times \frac{22}{7} \times 2^2}=16:1$

Hence The ratio of the surface area of this sphere to that of a small sphere is 16 : 1

#Learn more:

The radius of a sphere is 14 cm.it is melted to form smaller spheres each having a radius of 7 cm.what will be the ratio of surface areas of one small sphere to that of the larger sphere?

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