Question

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of paper for each
hat
What is the correct amount of paper Aubrey will need per hat? Explain Aubrey's mistake. Use 3.14 for pie
and round to the nearest inch.

Answer 1

Answer:

Option C. is the correct option.

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of paper for each hat.

Cone with diameter six inches and slant height eight inches.

What is the correct amount of paper Aubrey will need per hat? Explain Aubrey’s mistake. Use 3.14 for π and round to the nearest inch.

A.  About 70 in2; Aubrey found the surface area of the cone, but did not include the base.

B.  About 70 in2; Aubrey used the diameter instead of the radius to find the surface area of a cone.

C.  About 75 in2; Aubrey found the surface area of the cone and included the base.

D.  About 75 in2; Aubrey found the volume of the cone instead of the surface area.

Lateral surface area of a cone = Paper required to for each hat

Lateral surface area = πrl

Here r = radius of the cone

l = lateral height of the cone

Lateral surface area = π(3)(8)

                                 = 75.36 square inches

                                 ≈ 75 square inches

Therefore, total paper required for each cap is about 75 square inches.

Total surface area of the cone (Lateral area + Area of the base)

= πr(r + l)

= 3.14(3)(3 + 8)

= 103.62

≈ 104 square inches.

Aubrey did a mistake by finding the total surface area (including base area) of the cone instead of lateral surface area.

Therefore, option C. is the correct option.