Question

The radius of the base of a right circular cylinder is 1/7th of its height if the area of its curved surface is 176 sq .cm find its volume

Answer 1

The volume of the right circular cylinder is
`\( (44)/(3) \)` cubic centimeters.

Step-by-step explanation:

Let r be the radius of the base and h be the height of the right circular cylinder. According to the given information,
`\( r = (h)/(7) \)`. The formula for the curved surface area (CSA) of a cylinder is
`\( 2\pi rh \)`. Given that the CSA is 176 sq. cm, we can substitute
`\( r = (h)/(7) \)` into the formula:

`\[ 2\pi \left((h)/(7)\right)h = 176 \]`

Solving for h in the above equation gives h = 14 cm. Substituting this value of h into
`\( r = (h)/(7) \)` gives r = 2 cm. Now, using the formula for the volume of a cylinder
`\( V = \pi r^2 h \)`, we can calculate the volume:

`\[ V = \pi \left(2\right)^2 \cdot 14 = (44)/(3) \pi \]`

Thus, the volume of the right circular cylinder is
`\( (44)/(3) \)` cubic centimeters. This demonstrates the relationship between the radius, height, and volume of the cylinder, given the information about the curved surface area.