Acylinder and a rectangular prism have the same volume and the same height the base of the prism is a square with a side length of 9 cm
what is the approximate radius of the cylinder?
a. 4.5 cm
b. 5.1 cm
c. 12.9 cm
d. 25.8 cm

Option B

Step-by-step explanation:

The formula of the volume of a cylinder is:

Where the radius is "r" and the height is "h".

The formula of the volume of a rectangular prism is:

Where "A" is the area of the base and "h" is the heigth.

As both volumes are equal, you can write:

Find the area of the base, which is a square, with the formula:

Where "s" is the lenght of any side of the square.

Divide both sides of the equation by "h" (because the heights are equal) and solve for the radius:

≈5.1 cm

B. 5.1 cm

Step-by-step explanation:

Formula to calculate volume of prism with base of a square

V = l²(h)

where l is side of square

           h is height of prism

Formula to calculate volume of cylinder

V = πr² h

Given in the question that both have same volume and height so we will equate their volume

l²(h) = πr² h

and

plug given values in the variable

height will cancel out

81 = πr²

r² = 81/π

r = √81/π

r = 5.08 cm

r ≈ 5.1 cm