Question

A circular piece of paper of radius 20 cm is cut in half
and each half is made into a hollow cone by joining
the straight edges. Find the slant height and base
radius of each cone.

Answer 1

Given:

A circular piece of paper of a radius of 20 cm is cut in half and each half is made into a hollow cone by joining the straight edges.

To find:

Find the slant height and base radius of each cone.

Solution:

The radius of the circular piece of paper = 20 cm

Finding the slant height of each cone:

Since the straight edges of the semi-circular part is joined together to form a cone

∴ Slant height of the cone so formed = Radius of the circular piece = 20 cm

Thus, the slant height of the cone is → 20 cm.

Finding the base radius of each cone:

Let "r" cm be the base radius of each cone.

We have,

[Length of the base of each cone] = [Length of each semi-circular part of the original circular piece of paper]

⇒ $2 \pi r = \frac{2 \pi \times radius \:of\: original\:circle}{2}$

⇒ $2 r = \frac{2\times 20}{2}$

⇒ $2 r = 20$

⇒ $\bold{ r = 10\:cm}$

Thus, the base radius of each cone is → 10 cm.

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