Question

A cone paper hat is being made for a birthday party, with no gaps or overlaps of material. The radius of the base of the hat is 8 inches and it’s height is 15 inches.

About how many square inches of material is used for the hat?

The amount of material used is about __ in^2

Answer 1

The amount of material used is about 628.32 square inches.

Explanation:

so here we have the formula to find area of cone

A= πr(r+ (h²+r²))

r=8 in and h=15in

Answer 2

578.05 inch²

Explanation:

Calculating the circumference of the base and the area of the sides and adding them together will get the surface area of a cone.

A=πr², where r is the circle's radius, is the formula for calculating a circle's area. To calculate the area of the circular base, we utilize this formula.

The sector, or side, of the cone, is essentially a segment of a circle. The ratio of the cone's radius to its slant height, or r/s, determines the sector's size.

We take the area of the circle's section to get the sector's size.

A=πr²⋅s/r

this simplifies to πrs.

Then, we multiply the to determine the area of the side of the cone.

the total surface area of the cone =bottom face +side

=πr²+ πrs

= πr(r+s)

=π8(8+15) =578.05 inch²