Question

In the con of the problem, how does the volume of a cylinder with a radius of 4 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units?

a) The cylinder's volume is greater.

b) The rectangular prism's volume is greater.

c) The volumes are equal.

d) Not enough information to compare.

Answer 1

The volume of a cylinder with a radius of 4 units and a height of 12 units is greater than the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units.

Step-by-step explanation:

To compare the volume of a cylinder with the volume of a rectangular prism, we can use the formulas for each shape. The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. Substituting the given values (r = 4 and h = 12) into the formula gives V = 3.142 × (4)² × 12 = 602.112 units³.

The volume of a rectangular prism is given by V = lwh, where l, w, and h are the dimensions. Substituting the given values (l = 8, w = 8, and h = 6) into the formula gives V = 8 × 8 × 6 = 384 units³.

Therefore, the volume of the cylinder (602.112 units³) is greater than the volume of the rectangular prism (384 units³). So, the correct answer is a) The cylinder's volume is greater.