Question

A frustum is made by removing a small cone from a similar large cone in the diagram shown the height of a small cone is a quarter of the height of the large chrome work out the volume of the frustum

Answer 1

Answer:

Volume of the frustum = ⅓πh(4R² - r²)

Step-by-step explanation:

We are to determine the volume of the frustum.

Find attached the diagram obtained from the given information.

Let height of small cone = h

height of the large cone = H

The height of a small cone is a quarter of the height of the large cone:

h = ¼×H

H = 4h

Volume of the frustum = volume of the large cone - volume of small cone

volume of the large cone = ⅓πR²H

= ⅓πR²(4h) = 4/3 ×π×R²h

volume of small cone = ⅓πr²h

Volume of the frustum = 4/3 ×π×R²h -  ⅓πr²h

Volume of the frustum = ⅓(4π×R²h - πr²h)

Volume of the frustum = ⅓πh(4R² - r²)