Question

a cylinder has a radius of 3 cm and a height of 8 cm. what is the volume of the cylinder in terms of π? a. 54π cm³ b. 72π cm³ c. 18π cm³ d. 24π cm³ which of the following best describes why volume calculations are important in real - world scenarios? a. for measuring weight b. for determining capacity c. for measuring lengths d. for calculating speed

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 3\space cm\) and \(h=8\space cm\). Then \(V=\pi\times(3)^{2}\times8\).
First, calculate \((3)^{2}=9\). So \(V=\pi\times9\times8\).
Then, \(9\times8 = 72\). So \(V = 72\pi\space cm^{3}\).

For the second question:
Volume is a measure of the amount of space occupied by a three - dimensional object. Capacity is the amount that a container can hold, which is related to the volume of the container. Weight is measured in units like grams or kilograms (related to mass), lengths are measured in units like meters or centimeters, and speed is measured in units like meters per second.

Answer:

For the first question: B. \(72\pi\space cm^{3}\)
For the second question: B. For determining capacity