A paper cone has a base diameter of 8cm and a height of 3cm a volume of the cone in terms of pie d calculate height c calculate CSA in terms of pie

Answer 1

a) The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height. Since the cone has a base diameter of 8cm, the radius is 4cm. Thus, the volume of the cone is V = (1/3)π(4cm)^2(3cm) = 16π cm^3.

b) The formula for the curved surface area (CSA) of a cone is CSA = πrℓ, where ℓ is the slant height of the cone. To find the slant height, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. For the cone, the slant height is the hypotenuse, the height is one leg, and the radius is the other leg. Thus, using r = 4cm and h = 3cm, we have ℓ = √(r^2 + h^2) = √(4^2 + 3^2) = 5cm. Therefore, the CSA of the cone is CSA = π(4cm)(5cm) = 20π cm^2.