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 = }(\pi* r^2* 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}=(\pi*5.25^2*6.75)/(3)=194.83in^3 \end{gathered}`

Volume of a ball is given by

`\text{volume of ball =}(4)/(3)*\pi* r^3`

where r is the radius of the ball

in this case,

`r=(8(1)/(2))/(2)=4.25in`

Therefore

`\text{Volume of ball = }(4*\pi*4.25^3)/(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}`