To find the volume of the cone in the picture where S = 13 cm and R = 5cm
Step 1 ____
Step 2 ____
Step 3 ____
Find h by using the area of a triangle = (bh)/2
Find h by using the Pythagorean Theorem r ^ 2 + h ^ 2 = s ^ 2
Since h = 6 use the formula V = 1/3 * pi * r ^ 2 * h to find the volume
Since h = 12 , use the formula V = 1/3 * pi * r ^ 2 * h to find the volume
The volume is approximately 314.2c * m ^ 3
The volume is approximately 38.04c * m ^ 3
Step 1: Use the Pythagorean Theorem to find the height, h:
r^2 + h^2 = s^2
5^2 + h^2 = 13^2
25 + h^2 = 169
h^2 = 144
h = 12
Step 2: Calculate the volume using the formula V = (1/3) * π * r^2 * h:
V = (1/3) * π * 5^2 * 12
V = (1/3) * π * 25 * 12
V = (1/3) * π * 300
V = 100π
V ≈ 314.2 cm^3
Step 3: Calculate the volume using the formula V = (1/3) * π * r^2 * h with h = 6:
V = (1/3) * π * 5^2 * 6
V = (1/3) * π * 25 * 6
V = (1/3) * π * 150
V = 50π
V ≈ 157.1 cm^3
Therefore, the volume of the cone is approximately 314.2 cm^3 when h = 12 cm and approximately 157.1 cm^3 when h = 6 cm.