Problem

bhnmath.ca/wp-content/uploads/resources/Grade9-MTH1W1/EQAO/PracticeTest1/Interactive/index.html Scaffolded and Di... e p2nı Brightspace Resources Question 1 of 14 Q A cone and a cylinder have the same height and the same radius. If the volume of the cylinder is $162 \mathrm{~cm}^{3}$, what is the volume of the cone? $486 \mathrm{~cm}^{3}$ $81 \mathrm{~cm}^{3}$ $324 \mathrm{~cm}^{3}$ $54 \mathrm{~cm}^{3}$

Solution

Step 1 :Given the volume of the cylinder is \(162 \mathrm{~cm}^{3}\), and the cone and cylinder have the same height and radius.

Step 2 :The formula for the volume of a cylinder is \(V_{cylinder} = \pi r^2 h\), and the formula for the volume of a cone is \(V_{cone} = \frac{1}{3} \pi r^2 h\).

Step 3 :Since the cone and cylinder have the same height and radius, we can write the volume of the cone as \(V_{cone} = \frac{1}{3} V_{cylinder}\).

Step 4 :Substitute the given volume of the cylinder: \(V_{cone} = \frac{1}{3} (162)\).

Step 5 :Calculate the volume of the cone: \(V_{cone} = 54\).

Step 6 :\(\boxed{54 \mathrm{~cm}^{3}}\) is the volume of the cone.

From Solvely APP
Source: https://solvelyapp.com/problems/16012/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download