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Volume Calculation of Cylinders

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Questions and Answers

What is the volume of the smaller cylinder with a radius of 3 cm and the same height of 14 cm?

84.78 cm³

94 cm³

126 cm³ (correct)

84 cm³

What is the volume of the larger cylinder with a radius of 7 cm and height of 14 cm?

1540 cm³ (correct)

1470 cm³

616 cm³

324 cm³

What is the formula to calculate the volume of the remaining solid after carving out the smaller cylinder from the larger one?

Volume of remaining solid = Volume of larger cylinder - Volume of smaller cylinder (correct)

Volume of remaining solid = Volume of larger cylinder × Volume of smaller cylinder

Volume of remaining solid = Volume of smaller cylinder - Volume of larger cylinder

Volume of remaining solid = Volume of smaller cylinder + Volume of larger cylinder

After calculating the volumes, what is the volume of the remaining solid when the smaller cylinder is removed from the larger one?

<p>1410 cm³</p> Signup and view all the answers

Considering both cylinders have the same height, how does height affect the volume of a cylinder?

<p>Volume is directly proportional to height.</p> Signup and view all the answers

Study Notes

Problem Setup

We have two cylinders: a larger one and a smaller one carved out of it.
Both cylinders have the same height of 14 cm.
The larger cylinder has a radius of 7 cm.
The smaller cylinder has a radius of 3 cm.

Finding the Volume

We need to find the volume of the remaining solid.
This is achieved by subtracting the volume of the smaller cylinder from the volume of the larger cylinder.

Calculating Volumes

Volume of a cylinder: π * r^2 * h, where 'r' is the radius and 'h' is the height.
Volume of the larger cylinder: π * 7^2 * 14 = 686π cm^3
Volume of the smaller cylinder: π * 3^2 * 14 = 126π cm^3
Volume of the remaining solid: 686π - 126π = 560π cm^3

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Description

This quiz focuses on calculating the volume of two cylinders: a larger and a smaller one, both with the same height. You'll learn how to find the volume of the remaining solid by subtracting the smaller cylinder's volume from that of the larger cylinder using the formula for the volume of a cylinder.