The volume of each shape is 250 cubic inches.
A) Find the height of a cylinder with a radius of 3 inches.
250/3^2/ 3.14 = height of cylinder?
B)Find the radius of the sphere.
Is it just 3 inches?
C) Find the height of a cone with a radius of 3 inches.
I need help with this can someone please check if I'm doing this right?
A. V = pi*r^2 * h = 250 in^3
h =250 / pi*r^2 = 250 / 28.3 = 8.84 In.
B. V = (4/3)pi*r^3 = 250 In^3
r^3 = 250 / (4/3)pi = 250 / 4.19 = 59.7
r = 3.91 In.
C. V = (1/3)pi*r^2*h = 250 In^3
Solve for h.
A) To find the height of a cylinder with a volume of 250 cubic inches and a radius of 3 inches, you can use the formula for the volume of a cylinder: V = πr^2h. Rearranging the formula to solve for height, we get h = V / (πr^2).
Substituting the given values into the formula: V = 250 cubic inches and r = 3 inches, we get h = 250 / (π * 3^2). Evaluating the expression gives:
h = 250 / (π * 9)
h ≈ 8.841 inches
Therefore, the height of the cylinder is approximately 8.841 inches.
B) To find the radius of a sphere with a volume of 250 cubic inches, you need to use the formula for the volume of a sphere: V = (4/3)πr^3. Rearranging the formula to solve for the radius, we get r = ((3V) / (4π))^(1/3).
Substituting the given value of V = 250 cubic inches, we get r = ((3*250) / (4π))^(1/3). Evaluating the expression gives:
r = ((750) / (4π))^(1/3)
r ≈ 4.781 inches
Therefore, the radius of the sphere is approximately 4.781 inches.
C) To find the height of a cone with a volume of 250 cubic inches and a radius of 3 inches, you can use the formula for the volume of a cone: V = (1/3)πr^2h. Rearranging the formula to solve for height, we get h = (3V) / (πr^2).
Substituting the given values into the formula: V = 250 cubic inches and r = 3 inches, we get h = (3*250) / (π * 3^2). Evaluating the expression gives:
h = (750) / (π * 9)
h ≈ 8.841 inches
Therefore, the height of the cone is approximately 8.841 inches.
Note: The calculations for the height of the cylinder and the cone are the same because the volume and radius values are the same.
A) To find the height of a cylinder with a given volume, you can use the formula:
Volume of a cylinder = π * radius^2 * height
In this case, the volume is given as 250 cubic inches, and the radius is 3 inches. So, you can rearrange the formula to solve for height:
250 = π * 3^2 * height
Dividing both sides by π * 3^2, you get:
height = 250 / (π * 3^2)
Calculating this expression, you will get the height of the cylinder.
B) To find the radius of a sphere with a given volume, you can use the formula:
Volume of a sphere = (4/3) * π * radius^3
In this case, the volume is given as 250 cubic inches. So, you can rearrange the formula to solve for the radius:
250 = (4/3) * π * radius^3
Dividing both sides by (4/3) * π, you get:
radius^3 = 250 / [(4/3) * π]
To find the radius, you need to take the cube root of both sides:
radius = (250 / [(4/3) * π])^(1/3)
Evaluating this expression will give you the radius of the sphere.
C) To find the height of a cone with a given volume, you can use the formula:
Volume of a cone = (1/3) * π * radius^2 * height
In this case, the volume is given as 250 cubic inches, and the radius is given as 3 inches. So, you can rearrange the formula to solve for the height:
250 = (1/3) * π * 3^2 * height
Dividing both sides by (1/3) * π * 3^2, you get:
height = 250 / [(1/3) * π * 3^2]
Calculating this expression will give you the height of the cone.