# The total surface area of the cone is 136 pi, find the lateral surface area if the radius is 6 cm

March 28, 2021 | education

| It is known from the condition that the total surface area of the cone is 136n cm ^ 2. And we need to find the area of the lateral surface if the base radius is 6 cm.

Let’s start by recalling the formula for finding the total surface area of a cone:

S floor = nR ^ 2 + S side.

Let us express the lateral surface area from the formula:

S side = S floor – nR ^ 2.

We have enough data to calculate. We substitute the values into the formula and perform the calculations:

S side = 136p – n * 6 ^ 2 = 136p – 36p = 100p cm ^ 2.

Answer: 100n cm ^ 2.

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