Answer:
C. About 75 in²; Aubrey found the surface area of the cone and included the base.
Step-by-step explanation:
In the questions above we were given the following:
Cone with
Diameter(D) = 6 inches
Slant height (l) = 8 inches.
Aubrey made an error in her calculation.
She found the Total Surface area of the cone using the formula:
Total Surface Area of a cone = πrl + πr²
= πr(l + r)
The Total surface area of a cone is the calculated as Sum of the curved surface area of a cone and the base of the cone.
Where:
Curved surface area of the cone is calculated as = πrl
Base of a cone is calculated as = πr²
Where r = radius of the cone
l = slant height of the cone
In the question, we were given
slant height(l) = 8 inches.
radius = Diameter ÷ 2 = 6÷2 = 3 inches.
Using π = 3.14
Surface area = 3.14 × 3(8+3)
= 9.42 × 11
Surface area = 103.62 in²
Approximately to the nearest inch = 104 in² or 104 square inches.
But this answer is WRONG.
The RIGHT FORMULA Aubrey should have used is
Curved Surface Area or the Lateral Area of a Cone = πrL
slant height(l) = 8 inches.
radius = Diameter ÷ 2 = 6÷2 = 3 inches.
Using π = 3.14
Curved Surface Area of a Cone = πrL
= 3.14 × 3 inches × 8 inches
= 75.36 square inches or 75.36in²
Approximately to the nearest inch = 75 square inches or 75 in².
This is the correct answer.
The error Aubrey made was she calculated the Total surface area of the cone which includes the base of the cone instead of calculating the curved surface area of the cone only.
Hence, from the above calculation , we can see that Option C "About 75 in²; Aubrey found the surface area of the cone and included the base" is the correct option.
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