Question

the area of a circle is used in the calculation of volume for which shape?
a. pyramid
b. cylinder
c. cube
d. prism

Explanation:

• Pyramid: The base of a pyramid is a polygon (e.g., triangle, square), not a circle. The volume formula \(V=\frac{1}{3}Bh\) (where \(B\) is the area of the base polygon and \(h\) is the height) does not use the area of a circle.
• Cylinder: A cylinder has two circular bases. The volume formula \(V = Bh=\pi r^{2}h\) (where \(B=\pi r^{2}\) is the area of the circular base, \(r\) is the radius of the base, and \(h\) is the height of the cylinder). So, the area of a circle (\(\pi r^{2}\)) is used in its volume calculation.
• Cube: A cube has square - shaped faces. The volume formula \(V = s^{3}\) (where \(s\) is the side length of the cube) does not involve the area of a circle.
• Prism: The base of a prism is a polygon (e.g., triangle, rectangle). The volume formula \(V=Bh\) (where \(B\) is the area of the base polygon and \(h\) is the height of the prism) does not use the area of a circle.

Answer:

B. Cylinder