We want to find the of the given .
To do so, we must know that the lateral area of a right cone is half the product of the of the base and the .
L.A.=21⋅2πr⋅ℓ⇔L.A.=πrℓ
In this ,
r is the and
ℓ is the slant height of the cone. Since we know that the
d is equal to
8, we can divide it by
2 and get the radius of the base.
r=28 ⇒ r=4
With this information we are able to calculate the lateral area of the cone. To do so, we will substitute
r=4 and
ℓ=5 into the formula for the lateral area. Let's do it!
L.A.=πrℓ
L.A.=π(4)(5)
L.A.=π(20)
L.A.=20π
L.A.=62.831853…
L.A.≈62.8
The lateral area of the given cone, to the nearest tenth, is
62.8 square meters.