Question

Type the correct answer in each box. Use pi= 22/7, and round your answers to the nearest interger. The perimeter of the largest cross section of a sphere is 88 centimeters. The radius is 14 cm. The volume of the sphere is __ cm^3

Answer 1

r=14 cm

V=11499 cubic cm

Explanation:

If the radius of the sphere is r cm, then the perimeter of the largest cross section is the circumference of the circle qith radius r. Thus,

`88=2\pi r,\\ \\r=(88)/(2\pi)=(44)/(\pi)=(44)/((22)/(7))=(44)/(1)\cdot (7)/(22)=14\ cm.`

Thvolume of the sphere can be calculated using formula

`V=(4)/(3)\pi r^3.`

Since r=14 cm, we get

`V=(4)/(3)\cdot (22)/(7)\cdot 14^3=(4\cdot 22\cdot 2\cdot 14^2)/(3)=(34496)/(3)\approx 11499\ cm^3.`

Answer 2

11,499 cm^3

Explanation:

The volume of a sphere is given by the formula
`V=(4)/(3)\pi r^3`

The radius is given as 14, we plug it into the formula and find the volume:

`V=(4)/(3)\pi r^3\\V=(4)/(3)((22)/(7)) (14)^3\\V=11498.66`

rounded to nearest integer, the volume is 11,499