Question

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

Answer 1

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

Solution:

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

Therefore,

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

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

$377 = k \times 6^2 \times 10\\\\377 = 360 \times k\\\\k = \frac{377}{360}\\\\k = 1.047 \approx 1.05$

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

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

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