Question

From a wooden cylinder with volume 234 sq.cm a cone with radius of base and height as the cylinder is made .the volume of the wood in the left over object is

Answer 1

Given:

From a wooden cylinder with volume 234 cubic cm a cone with the radius of base and height as the cylinder is made

To find:

The volume of the wood in the left over object is?

Solution:

Let's assume,

"r" → base radius of the cylinder

"h" → height of the cylinder

Since the volume of the wooden cylinder = 234 cm³

∴ $\pi r^2 h = 234$

$\implies r^2h = \frac{234\:\times\: 7}{22}$ ...... (i)

It is given that,

[The base radius and height of wooden cylinder] = [The base radius and height of cone carved out from the cylinder]

Therefore,

The volume of the cone will be,

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

on substituting from (i), we get

= $\frac{1}{3} \times \frac{22}{7} \times \frac{234\:\times\: 7}{22}$

= $\bold{78 \:cm^3}$

Now,

The remaining volume of the wood from the object is,

= [Volume of the cylinder] - [Volume of the cone]

= 234 cm³ - 78 cm³

= 156 cm³

Thus, the volume of the wood in the leftover object is → 156 cm³.

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