Answer:
Step-by-step 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
Answer:
L = 163.4 m2; S = 213.6 m2
Step-by-step 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.
