Hollow Cylinder Volume Quiz

Study Notes

Hollow Cylinder Volume

The volume of a hollow cylinder is calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
The volume of a cylinder is given by πr²h, where r is the radius and h is the height.

Problem 116: Finding the Cylinder Thickness

The outer radius is 9 cm and height is 14 cm.
The volume of the metal used is 748 cm³.
The volume of the metal used is the difference between the volume of the outer cylinder and the volume of the inner cylinder.
The formula for this is πh(R² - r²), where R is the outer radius and r is the inner radius.
Substitute the known values and solve the equation to find the inner radius (r) which is 8 cm.
The thickness of the cylinder is the difference between the outer radius and inner radius, which is 1 cm.

Problem 117: Finding the Number of Cones

The cylindrical container has a diameter of 21 cm and a height of 38 cm.
Calculate the volume of ice cream in the cylinder using the formula πr²h, which is approximately 3829 cm³.
The cone has a height of 12 cm and a diameter of 7 cm.
The cone also has a hemispherical cap.
Calculate the volume of ice cream in one cone with a hemispherical cap, which is approximately 792 cm³
Divide the volume of ice cream in the cylinder by the volume of ice cream in one cone to get the number of cones needed, which is approximately 5.

Description

This quiz explores the concepts of volume calculations for hollow cylinders. It includes problems on determining the thickness of a cylinder through the difference in volumes and finding quantities related to cylindrical shapes. Test your understanding of these essential geometry concepts.