Question

Container A and container B are right circular cylinders. A has a radius of 4 inches and a height of 5 inches while container B has a radius of 2 inches and a height of 10 inches. Sarah pours equal amounts of oil into both containers and finds that the height of the oil in container A is 2 inches. What is the height of the oil in container B?
Okay I know I have to find the volume of both which I did (container A’s volume is 80pi and container B’s volume is 40pi) but I don’t know what to do after that. Can someone help me out?

Answer 1

Answer:

8 in

Step-by-step explanation:

RA = 4 in, RB = 2 in

oil height in A = hA = 2 in

Find oil height in B = hB

volume of oil in A = VA = π*RA² * hA

equal amount means volume of oil in B VB = VA

But VB = π*RB² * hB

so π*RA² * hA = π*RB² * hB

then

hB = hA *(RA/RB)² = 2 * (4/2)² = 8 in

Answer 2

Answer:

given that a right circular cylinder is 12 full of water, volume of water in the container is 36 cubic inches and the height of the container is 9 inches.

We have to find the diameter of the base of the cylinder in inches.

Let us first draw the diagram of the right circular cylinder:

Let,

r be the radius of the cylinder.

Since the container of a right circular cylinder is 12 full of water and height of the container is 9 inches then height of the water is =9(12)=4.5

Now, use the formula of volume of the right circular cylinder.

Volume of the cylinder=πr2(height)

Substitute 36 for volume and 4.5 for height in above equation.

⇒36=πr2(4.5)

Divide each side by 4.5

⇒8=πr2

Divide each side by π

⇒8π=r2

Take the square root on each side.

⇒8π=−−−−√r2−−√⇒8π−−√=r

Simplify further.

⇒r=22π−−√

Therefore, the radius of the cylinder is r=22π−−√ inches.

Since, the diameter is twice the length of the radius.

Thus, the diameter of the base of the cylinder=2r=2(22π−−√)=42π−−√ inches