Question

Nguyen is decorating the room for her sister’s baby shower party. She is wrapping Vietnamese conical hats in baby prints tissue paper to decorate the tables and some shelves in the wall. Each hat has a diameter of 16 inches and a height of 9 inches. If she wants to wrap 21 Vietnamese hats, how much tissue paper will she need?

A 4,176 in2

B 8,975 in2

C 10,580 in2

D 36,267 in2

Answer 1

The formula to calculate surface area of a conical hat in this case:

A = pi x radius x sqrt(radius^2 + height^2) + pi x radius^2

= pi x (16/2) x sqrt((16/2)^2 + 9^2)) + pi x (16/2)^2

= 503.7 (in2)

=> For 21 conical hats, Nguyen would need an amount of tissue paper:

A = 21 x 503.7 = 10577.7 (in2) = ~ 10580 (in2)

=> Option C is correct.

Hope this helps!

:)

Hi vọng là đáp án đúng!

:)

Answer 2

So the best and correct answer is C because this is how you do it The surface area of the cone has formula

pi * radius * ( radius + sqrt ( height^2 + radius^2)) =
pi * radius^2 + pi * radius * sqrt( height^2 + radius^2)

However, this includes the base of the cone and the hats do NOT have
that. "The hats are shaped like a cone with NO BASE", says the 3rd sentence.

So the formula becomes pi * radius * sqrt( height^2 + radius^2)

diameter = 16
radius = 8
height = 9

The surface area of ONE of the hats is pi * 8 * sqrt( 9^2 + 8^2)
= pi * 8 * sqrt( 81+64)
= pi * 8 * sqrt(145)
302.63828053.....


21 of them is 21 * 302... = 6355.40689112841343251026086.....