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
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.
To calculate the volume of the cone, you can use the formula V = (1/3) * π * r^2 * h, where V represents the volume, π represents the mathematical constant pi, r represents the radius of the base, and h represents the height.
Given that the base diameter is 8 cm, we can calculate the radius by dividing the diameter by 2: r = 8 cm / 2 = 4 cm.
Using the given height of 3 cm, we can substitute the values into the formula:
V = (1/3) * π * (4 cm)^2 * 3 cm = 16π cm^3.
Therefore, the volume of the cone is 16π cm^3.
To calculate the curved surface area (CSA) of the cone, we can use the formula CSA = π * r * l, where l represents the slant height of the cone.
To find the slant height (l), we can use the Pythagorean theorem, which states that the square of the hypotenuse (l) is equal to the sum of the squares of the other two sides (r and h).
Using the values we previously calculated, we can find l:
l^2 = r^2 + h^2
l^2 = (4 cm)^2 + (3 cm)^2
l^2 = 16 cm^2 + 9 cm^2
l^2 = 25 cm^2
l = √(25 cm^2) = 5 cm.
Now we can substitute the values into the formula for CSA:
CSA = π * 4 cm * 5 cm = 20π cm^2.
Therefore, the curved surface area of the cone is 20π cm^2.