Question

a cone shaped funnel can hold 314 cubic inches of water. if the height of the funnel is 12 inches what is the radius of the funnel

Answer 1

Answer: Radius = 5inches

Explanation:

Volume of a cone = 1/3πr²h

314 = 1/3 X 3.142 X r² X 12

314 = 37.704/3 X r²

314 = 12.568 X r²

r² = 314/ 12.568

r² = 24.9

r = √24.9

r = 4.98 ~ 5 inches

Answer 2

The radius of cone shaped funnel is 5 inches

Solution:

To calculate the volume of a cone, we have to multiply the base area, in this case the area of a circle:

`\pi r^2` by its height and by
`(1)/(3)`

`\bold{Volume \ of \ a \ cone \ is \ (1)/(3) * \pi* r^2* h}`

Here, volume = 314; h = 12;

we already know
`\bold{\pi=3.14}`

On substituting the vales we get,

`314=(1)/(3)* 3.14* r^2* 12`

Bringing 3.14 to the L.H.S,

`(314)/(3.14)=(1)/(3)* r^2*12`

On solving we get,

`100=4* r^2`

`(100)/(4)=r^2`

On dividing 100 and 4 we get,

`25=r^2`

Taking roots on both sides,

`\sqrt25=√(r^2)`

`√(5*5)=\r`

`\therefore r=5`

Hence, radius = 5 inches