204k views
2 votes
A cone has a lateral surface area of 62.8 square yards. If the slant height is 2 yards, what is the total surface area of the cone?

User Eirikvaa
by
8.1k points

1 Answer

5 votes

Final answer:

The total surface area of the cone is 7π square yards.

Step-by-step explanation:

To find the total surface area of the cone, we need to find the lateral surface area and add it to the base area.

The lateral surface area of a cone is given by the formula πrℓ, where r is the radius and ℓ is the slant height.

In this case, the lateral surface area is 62.8 square yards and the slant height is 2 yards.

So, the lateral surface area of the cone is π(2)(2) = 4π square yards.

The base area of a cone is given by the formula πr^2, where r is the radius.

Since the slant height is given, we can use the Pythagorean theorem to find the radius. The radius is the hypotenuse of a right triangle with the slant height as one of the legs and the height of the cone as the other leg.

Using the Pythagorean theorem, we have r^2 = (2)^2 - (1)^2 = 4 - 1 = 3.

Therefore, the radius is √3 yards.

The base area of the cone is then π(√3)^2 = 3π square yards.

The total surface area of the cone is the sum of the lateral surface area and the base area, 4π + 3π = 7π square yards.

User UnderemployedJD
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories