Question

A cone and its dimensions are shown in the diagram. What is the volume of the cone in cubic inches?

Answer 1

The exact value of the volume is equal to

`V=19(397)/(512)\pi\ in^(3)`

Explanation:

we know that

The volume of a cone is equal to

`V=(1)/(3)\pi r^(2) h`

we have

`D=5(5)/(8)\ in`

convert to an improper fraction

`D=5(5)/(8)\ in=(5*8+5)/(8)=(45)/(8)\ in`

`r=(45/8)/2=(45)/(16)\ in`

`h=7(1)/(2)\ in=(7*2+1)/(2)=(15)/(2)\ in`

substitute in the formula of volume

`V=(1)/(3)\pi ((45)/(16)^(2))((15)/(2))=(30,375)/(1,536)\pi\ in^(3)`

Simplify

`(30,375)/(1,536)=(29,184)/(1,536)+(1,191)/(1,536)=19(397)/(512)`

substitute

`V=19(397)/(512)\pi\ in^(3)`