Question

Find the length of the slant height of a cone with a radius of 15 cm and a surface area of 1884 square cm.

Answer 1

surface area of cone= pi *r *l
\[\pi \times 15 \times l=1884,l=\frac{ 1884 }{ 15 \pi }=\frac{ 1884 }{ 15 \times 3.14 }=\frac{ 1884\times 100 }{ 15 \times 314 } =40\]

Answer 2

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Answer 3

\(\large A_{cone} = \pi r^2 + \pi r l\)

Let's start with the surface of the base.

\(\large A_{base} = \pi r^2 = \pi \times (15~cm)^2 = 707~ cm^2\)

Subtract 707 cm^2 from the surface area, and you have the lateral surface area.

Lateral surface area = 1884 cm^2 - 707 cm^2 = 1177 cm^2

The lateral surface area = \(\pi r l\), and r = 15 cm.

\(\pi r l = 1177~cm^2\)

\(3.14159 \times 15~cm \times l = 1177~cm^2\)

Solve for \(l\)

Answer 4

l=25

Answer 5

Correct.

Answer 6

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