Calculating Volumes of 3D Shapes

In this tutorial, Mr. Masonette explains how to calculate the volume of various geometric solids, including cylinders, cones, and spheres. He demonstrates that the volume of a cone is one-third that of a cylinder with the same radius and height. The tutorial also covers calculating the volume of a sphere using its radius and finding the height of a cylinder given its volume and radius. The video concludes with a prompt to subscribe for more math tutorials.

What is the volume of a cone with the same height and radius as a cylinder of 78 cubic centimeters?

• 26 cubic centimeters

• 39 cubic centimeters

• 78 cubic centimeters

• 52 cubic centimeters

How many times the volume of a cone is the volume of a cylinder with the same height and radius?

• 4 times

• 3 times

• 2 times

• 5 times

What is the relationship between the volume of a cone and a cylinder with the same dimensions?

• The cone's volume is half of the cylinder's

• The cone's volume is the same as the cylinder's

• The cone's volume is one-third of the cylinder's

• The cone's volume is three times the cylinder's

If a sphere has a radius of 2.4 centimeters, what is its volume to the nearest cubic centimeter?

• 57 cubic centimeters

• 58 cubic centimeters

• 60 cubic centimeters

• 59 cubic centimeters

What formula is used to calculate the volume of a sphere?

• 4/3πr^3

• πr^2h

• πr^3

• 2πrh

What is the first step in calculating the volume of a sphere?

• Raise the radius to the third power

• Multiply the radius by π

• Multiply the radius by 4/3

• Divide the radius by 3

If the radius of a sphere is doubled, how does the volume change?

• It doubles

• It increases eightfold

• It triples

• It quadruples

Given a cylinder with a volume of 40 cubic meters and a radius of 1.2 meters, what is the height of the cylinder to the nearest tenth of a meter?

• 8.7 meters

• 8.8 meters

• 8.9 meters

• 9.0 meters

How do you isolate the height variable when calculating the height of a cylinder?

• Multiply both sides by the radius

• Divide both sides by the coefficient of height

• Add the volume to both sides

• Subtract the radius from both sides

What is the volume of a cylinder with a radius of 1.2 meters and a height of 8.8 meters?

• 45 cubic meters

• 40 cubic meters

• 35 cubic meters

• 30 cubic meters