Question

If the volume of a cone is 72 cm3

then the volume of a cylinder with same base

and height as that of the cone is

A) 524 cm3 B) 616 cm3

C) 144 cm3 D) 216 cm3​

Answer 1

Answer:

D) 216 cm³

Step-by-step explanation:

$\frac{1}{3} \pi {r}^{2} h = \pi {r}^{2} h$

72cm³=πr²h

216cm³

Answer 2

Given,

The volume of a cone is 72 $cm^{3}$

To find,

The volume of a cylinder with base and height same as that of the given cone.

Solution,

We can find the solution to this problem simply by following the below process.

To solve this question, firstly, we need to know how the volume for a cone and a cylinder are calculated.

So, first, let's consider a cone with height h and radius of the base be r. Then the formula to find out the volume of the cone is

$V_{c} = \frac{1}{3} \pi r^{2} h$

Further, for the same height and base radius of the cylinder, the volume is given by,

$V_{cyl} =\pi r^{2} h$

If we compare the above two equations, that is the formulae for $V_{c}$ and $V_{cyl}$, we can see that,

$V_c =\frac{1}{3} V_{cyl}$

⇒ $V_{cyl}=3*V_c$

As the volume of the cone $V_c$ is given as 72 $cm^{3}$

So, $V_{cyl}=3*72$

⇒ $V_{cyl}=216 cm^{3}$

Therefore, the volume of a cylinder with base and height same as that of the given cone will be 216 $cm^{3}$.