If the slant height of the cone is 24 cm and its height is 21 cm .then find the volume of the cone .

Question

Answer given is - 2970 ×3.14 cm ^3 

Answer 1

The volume of a cone is:

 

V = pi*r²*h/3

 

where:

• V = Volume
• pi = 3.14159...
• r == radius of the base circle of the cone
• h = height = 21 cm

 

We know everything except for r, the radius of the base circle.  We are given the slant height, s, of the cone.  We can use the slant height and the regular height to find r by noting that r, h, and s from a right triangle with r and h as the legs and s as the hypotenuse.  Applying Pythagorean Theorem:

 

r² + h² = s²

r² = s² - h²

r² = 24² - 21²

 

V = pi*(24²-21²)*21/3

 

Use your calculator to get the answer.  The units will be cm³.