Question

Water leaks from a crack in a vase at a rate of 0.5 cubic inch per minute. How long does it take for 20% of the water to leak from a full vase?

the cone is 4.8 inch in diameter. and 10 inches in height. the formula is (1/3) x 3.14 x radius squared x height.

Answer 1

To find the time for 20% of the water to leak from the vase, calculate the vase's volume, take 20% of that volume, and divide by the leak rate. The result is approximately 76 minutes for 20% of the water to leak out.

Step-by-step explanation:

The question is asking us to calculate the time it takes for a specified percentage of water to leak from a vase given the leak rate and the volume of the vase. First, using the formula for the volume of a cone, V = (1/3)πr^2h, we find the total volume of water the vase can hold. Then 20% of that volume will give us the amount of water that needs to leak out. Finally, dividing the 20% volume by the leak rate will provide us with the time needed for that amount of water to leak out.

Given that the diameter of the vase is 4.8 inches, the radius is half of that, 2.4 inches. The height of the vase is 10 inches. Thus, the total water volume V in cubic inches is:

V = (1/3)π(2.4 inches)^2(10 inches) = 60.288π cubic inches.

20% of V is:

0.20 × 60.288π cubic inches = 12.0576π cubic inches.

Given that the leak rate is 0.5 cubic inches per minute, the time, t, to leak 20% of the water is:

t = (12.0576π cubic inches) / (0.5 cubic inches/minute) ≈ 75.9827 minutes.

Therefore, it takes approximately 76 minutes for 20% of the water to leak from the full vase.

Answer 2

find total volume to find what amount is 20%
hack, is put the 20% in alreadyy to find 20% volume
20%=1/5

so
vcone=1/3(hpir^2)
times thath by 1/5
vcone=1/15(hpir^2)
d/2=r
given

4.8=d
4.8/2=d/2=r=2.4
10=h

V=1/15(10pi2.4^2)
V=1/15(10pi5.76)
V=1/15(57.6pi)
V=3.84pi
V=12.0637 cubic inches=20% of vase
0.5 cubc inches per min

0.5 times t=12.0637
divide both sides by 0.5
t=24.1237
about 24 minutes