Question

which formula represents the volume of a prism?
a. ( v = b\times h )
b. ( v = 2b + h )
c. ( v = l + w + h )
d. ( v=pi r^{2} )

Explanation:

Step1: Recall the volume formula of a prism

The volume of a prism is given by the product of the base area \(B\) and the height \(h\).

Step2: Analyze each option

• Option a: \(V = B\times h\) is the correct formula for the volume of a prism.
• Option b: \(V=2B + h\) is not a valid volume formula. Volume is a three - dimensional measure and should be a product (not a sum) of relevant dimensions.
• Option c: \(V=l + w+h\) is a sum of length, width and height. Volume should be a product (e.g., for a rectangular prism \(V = l\times w\times h\) where \(l\times w\) is the base area \(B\)).
• Option d: \(V=\pi r^{2}\) is the formula for the area of a circle (not a volume formula). The volume of a cylinder (a type of prism with circular base) is \(V=\pi r^{2}h\).

Answer:

A. \(V = B\times h\)