Question

The diameter of a sphere is measured to be 5.36 in. Find (a) the radius of the sphere in centimeters, (b) the surface area of the sphere in square centimeters, and (c) the volume of the sphere in cubic centimeters.

Answer 1

a) r = 6.81 cm : radius of the sphere

b) A = 582.78 cm² : surface area of the sphere

c) V = 1322.91 cm³ : volume of the sphere

Step-by-step explanation:

Formula to calculate the surface area of the sphere:

A = 4×π×r² Formula (1)

Formula to calculate the volume of the sphere:

V = (4/3)×π×r³ Formula (2)

Problem development

a)

d = 5.36 in

1 in = 2.54 cm

`d = 5.36 in * (2.54cm)/(1in) = 13.614 cm`

r = d/2

Where:

r: sphere radius (cm)

d: sphere diameter (cm)

r = 13.614/2 = 6.81 cm

b)

We replace in formula (1)

A = 4×π×(6.81)² = 582.78 cm²

c)

We replace in formula (2)

V = (4/3)×π×(6.81)³ = 1322.91 cm³