Find in terms of π the curved surface area of a cone with circular base diameter 10 cm and height 12cm

Answer 1

The curved surface area of a cone can be found using the formula:

CSA = πrℓ

where CSA is the curved surface area, r is the radius of the base, and ℓ is the slant height of the cone.

Given that the diameter of the base is 10 cm, the radius (r) can be found by dividing the diameter by 2:

r = 10 cm / 2 = 5 cm.

To find the slant height (ℓ), we can use the Pythagorean theorem. The slant height, height, and radius form a right triangle, with the height as one of the legs and the slant height as the hypotenuse. The radius is the other leg.

Using the Pythagorean theorem:

ℓ^2 = h^2 + r^2

ℓ^2 = 12 cm^2 + (5 cm)^2

ℓ^2 = 144 cm^2 + 25 cm^2

ℓ^2 = 169 cm^2

Taking the square root of both sides to solve for ℓ:

ℓ = √169 cm

ℓ = 13 cm.

Now, we can substitute the values for r and ℓ into the formula for CSA:

CSA = π(5 cm)(13 cm)

CSA = 65π cm^2.

Therefore, the curved surface area of the cone is 65π cm^2.