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Identify the lateral area and surface area of a right cone with diameter 8 m and slant height 13 m.

2 Answers

4 votes

Answer:

L = 163.4 m2; S = 213.6 m2

Explanation:

The lateral area of a right cone with radius r and slant height l is L=πrl.

The figure shows a right cone.

The diameter d of the circle is twice the radius r, so r=d2.

Substitute the given value of the diameter d=8 m.

r=82=4 m

Therefore, r=4 m.

Apply the formula for the lateral area of a right cone L=πrl.

Substitute the known values for the radius r=4 m and the slant height l=13 m.

L=π(4)(13)

Multiply.

L=52π m2

Use a calculator to approximate. Round your answer to the nearest tenth.

L≈163.4 m2

Therefore, the lateral area of the cone is about 163.4 m2.

The surface area of a right cone with lateral area L and base area B is S=L+B, or S=πrl+πr2.

The area of the base is πr2 because the base is a circle.

The figure shows a circle. The diameter of the circle is 8 meters.

Substitute the given value for the radius r=4 m.

B=π(4)2=16π m2

Therefore, B=16π m2.

To calculate the surface area of the cone, substitute the known values into the formula for surface area.

S=52π+16π=68π m2

Use a calculator to approximate. Round your answer to the nearest tenth.

S≈213.6 m2

Therefore, the surface area of the cone is about 213.6 m2.

User Tyler Biscoe
by
8.0k points
3 votes

Answer:

  • lateral area: 52π m² ≈ 163.4 m²
  • surface area: 68π m² ≈ 213.6 m²

Explanation:

The lateral area of a cone with radius r and slant height h is ...

LA = πrh

For your cone, the lateral area is ...

LA = π(4 m)(13 m) = 52π m² ≈ 163.4 m²

__

The surface area is found by adding the area of the circular base. That area is ...

A = πr² = π(4 m)² = 16π m² ≈ 50.3 m²

Then the cone's surface area is ...

52π m² +16π m² = 68π m² ≈ 213.6 m²

User Ahmed Ekri
by
8.6k points

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