Write whether True or False and justify your answer A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Question

Philoid · Accepted Answer

According to the question,

Let diameter of cylinder = 2r, then diameter of cone = 2r

⇒ radius of cylinder = 2r/2 = r, and radius of cone = 2r/2 = r

Let height of cylinder = h, then height of cone = h

Now, volume of cylinder = πr²h …(i) [by using the above values]

And volume of cone = 1/3 πr²h

Or

Volume of cone = 1/3 (πr²h) = 1/3 (Volume of cylinder) [by equation (i)]

⇒ Volume of cone = 1/3 (Volume of cylinder)

⇒ Volume of cylinder = 3 × Volume of cone

Thus, the volume of cylinder is three times the volume of cone.

Hence, it true.

Write whether True or False and justify your answerA cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Write whether True or False and justify your answer
A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.