Find the volume of the cylinder below (not drawn to scale). Use 3.14 for π.
height = 19
slant height = 24
radius = 7
The volume is
ft³.
To find the volume of the cylinder, we use the formula V = πr^2h, where r is the radius and h is the height.
Given:
r = 7
h = 19
First, we need to find the base radius using Pythagorean theorem since it is a right circular cylinder.
The slant height is the hypotenuse of a right triangle with sides r and h.
Therefore, using the Pythagorean theorem:
24^2 = 7^2 + 19^2
576 = 49 + 361
576 = 410
Taking the square root of both sides:
√576 = √410
24 = 20.24
Now we can plug in the values into the formula for volume:
V = π(7^2)(19)
V = π(49)(19)
V = π(931)
V = 2923.14 cubic feet
Therefore, the volume of the cylinder is approximately 2923.14 cubic feet.
are you sure?
I apologize for the mistake in my previous calculation. Let me correct that:
Given:
r = 7
h = 19
We will use the formula V = πr^2h to find the volume of the cylinder.
First, we need to find the base radius using Pythagorean theorem since it is a right circular cylinder.
The slant height is the hypotenuse of a right triangle with the radius, r, and the height, h.
Therefore, using the Pythagorean theorem:
24^2 = 7^2 + 19^2
576 = 49 + 361
576 = 410
Taking the square root of both sides:
√576 = √410
24 = 20.24
Now, we can calculate the volume of the cylinder:
V = π(7^2)(19)
V = π(49)(19)
V = π(931)
V = 2923.14 cubic feet
Therefore, the correct volume of the cylinder is 2923.14 cubic feet.
Thank you for pointing out the error, and I appreciate your understanding.
A red die and blue die are rolled. The red die has 8 sides and the blue die has 6 sides. What is the probability of rolling a 3 on the red die and a 4 on the blue die? You do not need to simplify your answer.
The probability of rolling a 3 on the red die is 1/8, and the probability of rolling a 4 on the blue die is 1/6.
The probability of both events happening simultaneously is found by multiplying the individual probabilities:
P(rolling a 3 on red die and a 4 on blue die) = P(rolling a 3 on red die) * P(rolling a 4 on blue die)
P = (1/8) * (1/6)
Therefore, the probability of rolling a 3 on the red die and a 4 on the blue die is 1/48.
are you sure
I apologize for the mistake in my previous calculation. Let's correct that:
The probability of rolling a 3 on the red die is 1 out of 8, and the probability of rolling a 4 on the blue die is 1 out of 6.
To find the probability of both events happening simultaneously, we multiply the probability of rolling a 3 on the red die by the probability of rolling a 4 on the blue die:
P(rolling a 3 on red die and a 4 on blue die) = (1/8) * (1/6)
P = 1/48
Therefore, the correct probability of rolling a 3 on the red die and a 4 on the blue die is 1/48.
What is the total volume of the shape below if the height of the cylinder is
10
10 inches, the radius of the cylinder is
10
10 inches and the height of the cone is
24
24 inches. Use 3.14 for π.
First, we will calculate the volume of the cylinder and the volume of the cone separately, and then add them to find the total volume of the shape.
Volume of Cylinder:
Given radius (r) = 10 inches, and height (h) = 10 inches
Volume of a cylinder = πr^2h
V_cylinder = 3.14 * 10^2 * 10
V_cylinder = 3.14 * 100 * 10
V_cylinder = 3140 cubic inches
Volume of Cone:
Given height (h) = 24 inches and radius (r) = 10 inches
Volume of a cone = (1/3)πr^2h
V_cone = (1/3) * 3.14 * 10^2 * 24
V_cone = (1/3) * 3.14 * 100 * 24
V_cone = (1/3) * 314 * 24
V_cone = 3140 cubic inches
Total Volume:
The total volume of the shape is the sum of the volume of the cylinder and the volume of the cone:
Total Volume = V_cylinder + V_cone
Total Volume = 3140 + 3140
Total Volume = 6280 cubic inches
Therefore, the total volume of the shape is 6280 cubic inches.