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?
A of side = πrS, where s = length of side
From the Pythagorean theorem,
S^2 = r^2 + h^2
I hope this helps.
Thanks
trt3
To find the lateral surface area of a cone, we need to calculate the circumference of the base and multiply it by the slant height of the cone.
First, let's find the circumference of the base. The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the base radius is 6 inches. So, the circumference of the base is:
C = 2π(6) = 12π inches
Next, we need to find the slant height of the cone. The slant height is the distance from the tip of the cone to any point on the circumference of the base. To calculate the slant height, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The height of the cone is given as 8 inches, and the radius of the base is 6 inches. Using the Pythagorean theorem, we can calculate the slant height as follows:
slant height^2 = height^2 + base radius^2
slant height^2 = 8^2 + 6^2
slant height^2 = 64 + 36
slant height^2 = 100
slant height = √100 = 10 inches
Now that we have the circumference of the base (12π inches) and the slant height (10 inches), we can calculate the lateral surface area of the cone.
Lateral Surface Area = Circumference of Base × Slant Height
Lateral Surface Area = 12π inches × 10 inches ≈ 120π square inches
To find the answer to the nearest square inch, we can use an approximation for π. Let's use 3.14.
Lateral Surface Area ≈ 120π square inches ≈ 120 × 3.14 square inches
Lateral Surface Area ≈ 376.8 square inches
Therefore, to the nearest square inch, the area of the lateral surface of the cone is approximately 377 square inches.