Question

layla is filling up a cylindrical water bottle with a radius of 3 cm and a height of 10 cm. she wants to calculate how much water it can hold. question 1 what is the formula for the volume of a cylinder? v = 1/4 πr²h v = 4πr³ v = πr²h v = lwh

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by the product of the area of the base (a circle with area \( A=\pi r^{2} \)) and the height \( h \) of the cylinder.

Step2: Analyze each option

• Option \( V = \frac{1}{4}\pi r^{2}h \): This formula is not the standard volume formula for a cylinder.
• Option \( V = 4\pi r^{3} \): This formula is not related to the volume of a cylinder. The formula \( V=\frac{4}{3}\pi r^{3} \) is for the volume of a sphere.
• Option \( V=\pi r^{2}h \): This is the correct formula as \( V = (\text{Area of base})\times(\text{height})=\pi r^{2}h \).
• Option \( V = lwh \): This is the formula for the volume of a rectangular - prism (where \( l\) is length, \( w\) is width and \( h\) is height).

Answer:

\( V=\pi r^{2}h \) (the third option).