Question

A party hat shaped like a cone requires about 66 square inches ( Surface Area ) of paper to make. If the slant height is 7 inches, how wide is the hat?

Answer 1

6 inches

Explanation:

Solving

• Curved Area = π x r x slant height
• 66 = 3.14 x 7 x r
• r = 66/21.98 ≅ 3 inches

Width of the hat

• Diameter of the cone
• 2 x Radius
• 2 x 3 = 6 inches

Answer 2

6.00 in (nearest hundredth)

Explanation:

Lateral surface area = surface area excluding the bases(s)

Lateral surface area of a cone =
`\pi rs`

(where r is the radius and s is the slant height)

Given:

• lateral surface area ≈ 66 in²
• slant height (s) = 7 in

`\implies 66= \pi r \cdot 7=7 \pi r`

`\implies r=(66)/(7 \pi)`

The width of the hat is the diameter. As diameter = 2r:

`\begin{aligned}\implies \textsf{width} & =2 \cdot (66)/(7 \pi)\\\\ & =(132)/(7 \pi)\\\\ & = 6.00\: \sf in\:(nearest\:hundredth)\end{aligned}`