Find the surface area of a right circular cone with radius of 5cm and height of 12cm.
Do you want the area to include the circular base?
If so, that's a simple addition of the area of the circle
for just the sides,
SA = πrl, where l is the slant height
l^2 = 5^2 + 12^2
l = 13
SA = π(5)13)
= 65π
To find the surface area of a right circular cone, you need to calculate the curved surface area and the base area, and then add them together.
Here are the steps to find the surface area of a right circular cone with a radius of 5cm and height of 12cm:
1. Start by calculating the slant height of the cone using the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle formed by the height (h) and the radius (r) of the cone. Since r = 5cm and h = 12cm, you can use the formula l = √(r^2 + h^2) to find the slant height.
l = √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13cm
2. Calculate the curved surface area of the cone. The curved surface area (A) is given by the formula A = πrl, where r is the radius of the base and l is the slant height.
A = π * 5cm * 13cm
≈ 65π cm²
3. Calculate the base area of the cone. The base area (B) is given by the formula B = πr^2.
B = π * (5cm)^2
= 25π cm²
4. Add the curved surface area and the base area to find the total surface area (T) of the cone.
T = A + B
= 65π cm² + 25π cm²
= 90π cm²
Therefore, the surface area of the right circular cone with a radius of 5cm and height of 12cm is approximately 90π cm².