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

Answer:

11,499 cm^3

Step-by-step explanation:

The volume of a sphere is given by the formula  $V=\frac{4}{3}\pi r^3$

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

$V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}(\frac{22}{7}) (14)^3\\V=11498.66$

rounded to nearest integer, the volume is 11,499

Answer 2

Answer:

r=14 cm

V=11499 cubic cm

Step-by-step 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,

$88=2\pi r,\\ \\r=\dfrac{88}{2\pi}=\dfrac{44}{\pi}=\dfrac{44}{\frac{22}{7}}=\dfrac{44}{1}\cdot \dfrac{7}{22}=14\ cm.$

Thvolume of the sphere can be calculated using formula

$V=\dfrac{4}{3}\pi r^3.$

Since r=14 cm, we get

$V=\dfrac{4}{3}\cdot \dfrac{22}{7}\cdot 14^3=\dfrac{4\cdot 22\cdot 2\cdot 14^2}{3}=\dfrac{34496}{3}\approx 11499\ cm^3.$