To find the volume of the cone in the picture where S = 13 cm and R = 5 cm:
Step 1:
Step 2:
Step 3:
Word Bank:
The volume is approximately 314.16 cm^3
Since h = 6, use the V = (1/3)(pi)(r^2)(h) to find the volume
Since h = 12, use the V = (1/3)(pi)(r^2)(h) to find the volume
The volume is approximately 38.04 cm^3
Find h by using the Pythagorean Theorem: r^2 + h^2 = s^2
Find h by using the area of a triangle = (b x h)/2
Step 1: Find h by using the Pythagorean Theorem: r^2 + h^2 = s^2
Step 2: Use the V = (1/3)(pi)(r^2)(h) to find the volume
Step 3: The volume is approximately 314.16 cm^3
To find the volume of the cone in the picture, we can follow these steps:
Step 1: Find the height (h) of the cone using the Pythagorean Theorem.
The Pythagorean Theorem 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.
In this case, the hypotenuse is the slant height (S) of the cone, and the radius (R) is one of the other sides. Using the formula r^2 + h^2 = s^2, we can substitute the given values R = 5 cm and S = 13 cm to solve for h.
Step 2: Once we have the height of the cone, we can use the formula to find its volume.
The volume (V) of a cone is given by the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height. Plug in the values we have, R = 5 cm and h from Step 1, and perform the calculations to find the volume of the cone.
Step 3: Write the final answer in the appropriate units.
The volume should be stated in cubic centimeters (cm^3).
The word bank provided contains the possible solutions to the problem. The correct solution is to use Step 1 to find the height (h) of the cone, and then use Step 2 with the calculated height to find the volume. The correct answer from the word bank is "The volume is approximately 314.16 cm^3".
Step 1: Find h by using the Pythagorean Theorem: r^2 + h^2 = s^2
Given that R = 5 cm and S = 13 cm, we can use the Pythagorean Theorem to find h.
Plugging in the values, we have 5^2 + h^2 = 13^2.
Simplifying, we get 25 + h^2 = 169.
Subtracting 25 from both sides, we have h^2 = 144.
Taking the square root of both sides, we find h = 12 cm.
Step 2: Substitute the values of R = 5 cm and h = 12 cm into the formula for the volume of a cone: V = (1/3)(pi)(r^2)(h).
Plugging in the values, we have V = (1/3)(pi)(5^2)(12).
Simplifying, we get V = (1/3)(pi)(25)(12).
Multiplying, we find V = (1/3)(pi)(300).
Further simplifying, we have V = 100(pi) cm^3.
Step 3: Calculate the approximate value of the volume using the approximation for pi.
Using the approximation pi ≈ 3.1416, we can calculate the approximate value of the volume.
Plugging in the value, we have V ≈ 100(3.1416).
Multiplying, we find V ≈ 314.16 cm^3.
Therefore, the volume of the cone in the picture, with S = 13 cm and R = 5 cm, is approximately 314.16 cm^3.