The radius and height of a cylinder are in ratio 5:7 and it's volume is 550 square cm. Find its radius?

Question

Answer

Given information:

The radius and height of a cylinder are in the ratio 5:7.
The volume of the cylinder is 550 square cm.

Formula for the volume of a cylinder:

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.

Step-by-step solution:

Step 1: Set up the ratio between the radius and height:

Let the radius of the cylinder be 5x and the height be 7x, where x is a constant.

Step 2: Calculate the volume of the cylinder:

Using the formula for the volume of a cylinder, we have:
V = π(5x)^2(7x)
550 = 25πx^2(49x)
550 = 1225πx^3

Step 3: Solve for x:

Divide both sides of the equation by 1225π to isolate x:
550/(1225π) = x^3
x^3 = 550/(1225π)

Step 4: Find the value of x:

Take the cube root of both sides to solve for x:
x = (550/(1225π))^(1/3)

Step 5: Calculate the radius:

Substitute the value of x back into the expression for the radius:
radius = 5x
radius = 5 * (550/(1225π))^(1/3)

Step 6: Simplify the expression for the radius:

Use a calculator to evaluate the expression for the radius and round to the desired number of decimal places.

Answer:

The radius of the cylinder is approximately equal to the calculated value obtained in Step 6.