Question

The volume of cone is 30cm3 then the volume of cylinder having same base and same height

Answer 1

The volume of a cone is 30 cm³ then the volume of a cylinder having the same base and same height is 90 cm³.

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Let's understand a few concepts:

To solve the above problem we will use the following formulas:

$\boxed{\bold{Volume\:of\:cone = \frac{1}{3} \pi r^2h}}$

$\boxed{\bold{Volume\:of\:cylinder = \pi r^2 h}}$

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Let's solve the given problem:

The volume of the cone = 30 cm³

From the above formula of the volume of a cone, we get

$\frac{1}{3} \pi r_1^2 h_1 = 30 \:cm^3 \\\\\implies \pi r_1^2 h_1 = (30\times 3) \:cm^3\\\\\implies \pi r_1^2 h_1 = 90 \:cm^3\:.\:.\:.\:(1)$

From the above formula of the volume of a cylinder, we get

The volume of the cylinder = $\pi r_2^2 h_2 \:.\:.\:.\:(2)$

Here we are given that the base radius and height of the cylinder are the same as the base radius and height of the given cone.

i.e., r₁ = r₂ and h₁ = h₂ . . . (3)

Therefore, by comparing equations (1), (2) and (3), we get

$\pi r_1^2 h_1 = \pi r_2^2 h_2$

$\implies \pi r_2^2 h_2 = 90\:cm^3$

$\implies \bold{Volume \:of \:cylinder = 90\:cm^3}$

Thus, if the volume of a cone is 30 cm³ then the volume of a cylinder having the same base and same height is 90 cm³.

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Answer 2

Answer:

volume of cylinder r²h=30cm³

Step-by-step explanation:

volume of cone

1/3 r²h=1/3×30

=10cm³