The radius of a small ball is around 2.8436 cm. The radius of a basketball is about 4.22 times larger. What is the ratio of the surface areas of the small ball and a basketball? Part 2 What is the ratio of their volumes?

Explanation:

Both small ball and a basketball are in form of a sphere. Total surface area of a sphere is gotten using the formula;

surface area of a sphere S = 4πr²

If the radius of a small ball is around 2.8436 cm, its total surface area will be:

S = 4π(2.8436)²

S =4π(8.086)

S = 101.61 cm²

If the radius of a basketball is about 4.22 times larger, the radius will be 4 times larger as well. The radius of the basket ball = 4.22*2.8436

radius of thr basketball = 11.99cm

Surface area of the basketball S2 =  4π(11.99)²

S2 =4π(143.76)

S2 =1806.54cm²

The ratio of the surface areas of the small ball and a basketball S:S2

S:S2 = 101.61 cm² : 1806.54cm²

S:S2 = 0.0562

Hence, the ratio of the surface areas of the small ball and a basketball is approximately 0.0562.

2) The volume of a sphere = 4/3πr³

Volume of the small ball = 4/3π(2.8436)³

Volume of the small ball = 4/3 π  * 22.994

Volume of the small ball= 96.315cm³

Similarly;

Volume of the basketball = 4/3π(11.99)³

Volume of the small ball = 4/3 π  * 1723.68

Volume of the small ball= 7220.14cm³

The ratio of the volume of the small ball and a basketball V:V2

V:V2 = 96.315  : 7220.14

V:V2 = 0.01333

Hence, the ratio of the volumes of the small ball and a basketball is approximately 0.01333

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