Answer:
Step-by-step 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