The base radius of a cone is 6 inches, and the cone is 8 inches tall. To the nearest square inch, what is the area of the lateral surface of the cone?

Well, prepare yourself for a cone-tastic answer! The formula for the lateral surface area of a cone is A = πrl, where r is the radius and l is the slant height. But we can find l using some Pythagorean magic! Let's solve it together!

So, we know the height of the cone is 8 inches, and the radius is 6 inches. Using the Pythagorean theorem, we can find the slant height:

l² = r² + h²
l² = 6² + 8²
l² = 36 + 64
l² = 100
l = 10

Now, we can go back to our lateral surface area formula:

A = πrl
A = π(6)(10)
A = 60π

But wait! We need to round our answer to the nearest square inch. Since π is approximately 3.14, we can estimate:

A = 60(3.14)
A ≈ 188.4

So, to the nearest square inch, the area of the lateral surface of the cone is approximately 188 square inches. Enjoy your cone-venient answer!

To find the area of the lateral surface of the cone, we need to calculate the slant height first.

Using the Pythagorean theorem, we can find the slant height of the cone:

Slant height (l) = √(base radius squared + height squared)
= √(6^2 + 8^2)
= √(36 + 64)
= √100
= 10 inches

Next, to find the area of the lateral surface, we can use the formula:

Lateral surface area = π * base radius * slant height

Substituting the values we have:

Lateral surface area = π * 6 * 10
= 60π square inches

To get the answer to the nearest square inch, we can use the value of π as approximately 3.14:

Lateral surface area ≈ 60 * 3.14
≈ 188.4 square inches

Therefore, the area of the lateral surface of the cone, to the nearest square inch, is approximately 188 square inches.

To find the lateral surface area of a cone, you need to know the slant height (l) and the radius (r) of the cone.

In this case, the radius (r) is given as 6 inches, and the height (h) is given as 8 inches. However, we need to find the slant height to calculate the lateral surface area.

To find the slant height (l), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c^2 = a^2 + b^2.

In a cone, the slant height is the hypotenuse, the radius is one of the sides (a), and the height is the other side (b). So, we can rewrite the equation as l^2 = r^2 + h^2.

Replacing the given values, we have:
l^2 = 6^2 + 8^2
l^2 = 36 + 64
l^2 = 100

Taking the square root of both sides, we find:
l = √100
l = 10

Now we have the slant height (l) and the radius (r), so we can calculate the lateral surface area (A) using the formula: A = π * r * l.

Replacing the values, we have:
A = π * 6 * 10
A = 60π

To find the area to the nearest square inch, we need to find the numerical value of π, which is approximately 3.14159.

Therefore, the lateral surface area of the cone is approximately:
A = 60 * 3.14159
A ≈ 188.496

To the nearest square inch, the area is 188 square inches.

Total surface area = πrs + πr^2

Since πr^2 is the area of base, πrs = area of lateral surface.

Use Pythagorean Theorem to find s, the distance along the side from tip to base.

s^2 = h^2 + r^2

I'll let you do the calculations.