A cylinder. The radius is labeled r and the height is labeled h. Which formula can be used to find the volume of the cylinder? Check all that apply. A = ( d )( h ) V = B( h ) V = ( l )( w )( h ) V = 2( r )( h ) V = (pi) (r squared) (h)
The Correct Answer and Explanation is:
The formula for finding the volume of a cylinder is:V=πr2hV = \pi r^2 hV=πr2h
Let’s go through the options:
- A = (d)(h): This is incorrect. The formula for the area of a circle is A=πr2A = \pi r^2A=πr2, and this formula doesn’t account for the cylinder’s volume. Also, the term “d” is not a recognized variable for calculating volume.
- V = B(h): This is a correct formula, where BBB represents the area of the base of the cylinder (which is a circle). The area of a circle is B=πr2B = \pi r^2B=πr2, so when you multiply this by the height hhh, it gives the volume:
V=πr2hV = \pi r^2 hV=πr2h
This is another valid way to express the formula, where the area of the base B=πr2B = \pi r^2B=πr2.
- V = (l)(w)(h): This formula is for the volume of a rectangular prism, not a cylinder. The cylinder has a circular base, not a rectangular one, so this formula doesn’t apply here.
- V = 2(r)(h): This is incorrect. There’s no factor of 2 in the formula for the volume of a cylinder. The volume depends on the area of the circular base, which involves r2r^2r2, not rrr alone.
- V = πr2h\pi r^2 hπr2h: This is the correct formula for the volume of a cylinder. It uses the area of the circular base πr2\pi r^2πr2 and multiplies it by the height hhh.
So, the correct formula for the volume of a cylinder is V = πr2h\pi r^2 hπr2h, and the other option that can also be used is V = B(h), where B=πr2B = \pi r^2B=πr2.
