The given solid is a with a of
16.5 feet and a of
9.5 feet. To calculate the , we must know that the lateral area of a right cone is half the product of the of the base and the slant height.
L.A.=21⋅2πr⋅ℓ⇔L.A.=πrℓ
In this formula,
r is the and
ℓ is the slant height of the cone. We know that the diameter of the cone's base is
16.5 feet. By dividing by
2, we get the radius of the base.
r=216.5 ⇒ r=8.25 ft
We now know that the radius of the cone is
8.25 ft and that the slant height of the cone is
9.5 ft. With this information we are able to calculate the lateral area of the cone. To do so, we will substitute
r=8.25 and
ℓ=9.5 into the formula for the lateral area. Let's do it!
L.A.=πrℓ
L.A.=π(8.25)(9.5)
L.A.=π(78.375)
L.A.=78.375π
L.A.=246.222324…
L.A.≈246.2
The lateral area of the given cone, rounded to the nearest tenth, is
246.2 ft2.