The volume of a container varies jointly with the square of its radius, r, and its height, h. The container has a height of 10 centimeters, and radius of 6 centimeters, and a vo…

Question

asked May 15, 2021 208k views

1 Answer

Debasish Ghosh · Answer 1 · 2021-05-20T22:51:47+0000

Solution:

The volume of a container varies jointly with the square of its radius, r, and its height, h

Therefore,

$v \propto r^2h\\\\v = k * r^2h ----------- eqn\ 1$

The container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic centimeters

Substitute v = 377 and h = 10 and r = 6 in eqn 1

$377 = k * 6^2 * 10\\\\377 = 360 * k\\\\k = (377)/(360)\\\\k = 1.047 \approx 1.05$

What is the volume of a container with a radius of 4 centimeters and a height of 4 centimeters?

Substitute k = 1.05 and r = 4 and h = 4 in eqn 1

$v = 1.05 * 4^2 * 4\\\\v = 1.05 * 16 * 4\\\\v = 67.2$

Thus volume of a container with a radius of 4 centimeters and a height of 4 centimeters is 67.2 cubic centimeter