Question

the cone has a diameter of 10.5 inches and height of 6.75 inches. what is the volume of the cone? (hundredths place)the ball has a diameter of 8 1/2inches what Is the volume of the sphere? (hundredths place)the difference between the two volumes is(round to the nearest hundredth)

Answer 1

$\text{volume of cone = }\frac{\pi\times r^2\times h}{3}$

where,

r is the base radius of the cone

h is the perpendicular height of the cone

In this case,

r = 10.5 / 2= 5.25in

h = 6.75in

$\begin{gathered} \text{Therefore} \\ \text{volume of cone}=\frac{\pi\times5.25^2\times6.75}{3}=194.83in^3 \end{gathered}$

Volume of a ball is given by

$\text{volume of ball =}\frac{4}{3}\times\pi\times r^3$

where r is the radius of the ball

in this case,

$r=\frac{8\frac{1}{2}}{2}=4.25in$

Therefore

$\text{Volume of ball = }\frac{4\times\pi\times4.25^3}{3}=321.56in^3$

$\begin{gathered} \text{The difference betw}een\text{ the two volumes=321.56-194.83}=126.73 \\ =126.73in^3 \end{gathered}$