Question

Jane plans to make a conical party hat for her brother's birthday. Each party hat has a radius of 4 in and height of 23 in. How much material does she need if she wants to make 25 hats?

Answer 1

Given:

Jane plans to make a conical party hat for her brother's birthday. Each party hat has a radius of 4 in and a height of 23 in. How much material does she need if she wants to make 25 hats?

To find:

How much material does she need if she wants to make 25 hats?

Solution:

The radius of the conical hat, r = 4 in.

The height of the conical hat, h = 23 in.

∴ The slant height, $l = \sqrt{h^2 + r^2} = \sqrt{23^2 + 4^2} = 23.34 \:in.$

We have the formula of the Curved Surface Area of a Cone as follows:

$\boxed{\bold{C.S.A. \:of\:a\:cone = \pi r l}}$

Now, on substituting the values of l and r in the above formula, we get

The area of material required to make the conical hat is,

= C.S.A. of the conical hat

= $\frac{22}{7} \times 4\times 23.34$

= $\bold{293.41\:in.^2}$

Therefore,

The area of the material required for such 25 hats will be,

= 25 × 293.41 in.²

= 7335.25 in.²

Thus, she needs 7335.25 square inches of material if she wants to make 25 hats.

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