Question

A cylinder has a radius of 3 feet and a height of 7 feet. Which of the following can be used to calculate the volume of a cone that fits exactly inside the cylinder?

A. (3.14)(72)(3)
B. 1 over 3 (3.14)(72)(3)
C. (3.14)(32)(7)
D. 1 over 3 (3.14)(32)(7)

Answer 1

Volume of Cylinder: (3.14)r^2*h
Volume of cone: 1/3(3.14)r^2h

To fit exactly, both of the shapes' radii must be equal (have the same base) and must be equal in height

Therefore the equation would be 1/3(3.14)(3)^2*7

This equals 1/3(3.14)(9)(7)
Which equals 1/3(3.14)(63)

Again, it doesn't seem to answer any of the sections (correct me if I'm wrong)

Answer 2

D.
`(1)/(3) *3.14*3^(2) *7`

Explanation:

Given :

A cylinder having radius = 3 feet

Height = 7 feet

To Find : the volume of a cone that fits exactly inside the cylinder

Solution :

Refer the attached figure then you can observe that when the radius and height of the cone will be equal to radius and height of the cylinder only then cone fits exactly inside the cylinder

Now to check which of the following option is that volume of the cone that fits into the given cylinder .

Volume of cone =
`(1)/(3) \pi r^(2) h` ---(a)

where
`\pi =3.14`

now r (radius) and h(height) in this formula should be equal to r and h of the given cylinder

Consider Option A : VOLUME OF CONE :
`3.14*7^(2) *3`

If we compare this option with the formula (a)

first this is not the volume of cone since 1/3 is missing

Then r = 7 and h = 3

while r =3 and h = 7 of given cylinder

So option A cone cannot get fits into the given cylinder .

Thus option A is wrong .

Consider Option B : VOLUME OF CONE :
`(1)/(3) *3.14*7^(2) *3`

If we compare this option with the formula (a)

Then r = 7 and h = 3

while r =3 and h = 7 of given cylinder

So option B cone cannot get fits into the given cylinder .

Thus option B is wrong .

Consider Option C : VOLUME OF CONE :
`3.14*3^(2) *7`

If we compare this option with the formula (a)

We will see that this is not the volume of cone since 1/3 is missing

Thus the option C is wrong

Consider Option D : VOLUME OF CONE :
`(1)/(3) *3.14*3^(2) *7`

If we compare this option with the formula (a)

formula used is correct

and r = 3 and h = 7

Since r and h of this volume of cone is equal to r and h of given cylinder . So, this cone fits into given cylinder .

Thus Option D IS CORRECT .