How much larger is the calculation of the volume of a sphere’s whose radius is 45 inches if
is used instead of 3.14 ?
Round your answer to the nearest tenth.
The difference of using
rather than 3.14 is about cubic inches.
The formula for the volume of a sphere is V = (4/3)πr^3.
Using π = 3.14, the volume of the sphere with a radius of 45 inches would be:
V = (4/3)(3.14)(45)^3
V ≈ 381703.92 cubic inches
Using π = 3.14159, the volume of the sphere with a radius of 45 inches would be:
V = (4/3)(3.14159)(45)^3
V ≈ 382019.68 cubic inches
The difference in volume when using 3.14159 instead of 3.14 is about 315.8 cubic inches.
What is the total volume of the shape below if the height of the cylinder is 7 inches, the radius of the cylinder is 6 inches and the height of the cone is 27 inches. Use 3.14 for
To find the total volume of the shape, first calculate the volume of the cylinder and the volume of the cone separately, and then add them together.
Volume of a cylinder formula: V_cylinder = πr^2h
Volume of a cone formula: V_cone = (1/3)πr^2h
Given:
Radius of cylinder, r = 6 inches
Height of cylinder, h = 7 inches
Height of cone, h_cone = 27 inches
1. Calculate the volume of the cylinder:
V_cylinder = 3.14 * 6^2 * 7
V_cylinder = 3.14 * 36 * 7
V_cylinder = 791.04 cubic inches
2. Calculate the volume of the cone:
V_cone = (1/3) * 3.14 * 6^2 * 27
V_cone = (1/3) * 3.14 * 36 * 27
V_cone = 905.28 cubic inches
3. Add the volumes of the cylinder and the cone to get the total volume:
Total Volume = V_cylinder + V_cone
Total Volume = 791.04 + 905.28
Total Volume = 1696.32 cubic inches
The total volume of the shape is 1696.32 cubic inches.
A semi-sphere sits on top of a cylinder. The height of the cylinder is 34 feet and the diameter of the cylinder is 29 feet. What is the total volume? Use 3.14 for
. Round your answer to the nearest whole number. Click Here for Help Video
The total volume of the silo is cubic feet.
To find the total volume of the shape, we need to calculate the volume of the cylinder and the volume of the semi-sphere separately and then add them together.
Given:
Height of the cylinder (h_cylinder) = 34 feet
Diameter of the cylinder (d_cylinder) = 29 feet
1. Radius of the cylinder (r_cylinder) = d_cylinder / 2 = 29 / 2 = 14.5 feet
Volume of a cylinder formula: V_cylinder = πr^2h
Calculate the volume of the cylinder:
V_cylinder = 3.14 * (14.5)^2 * 34
V_cylinder = 3.14 * 210.25 * 34
V_cylinder = 22560.71 cubic feet
2. The height of the semi-sphere is equal to the radius of the cylinder, which is 14.5 feet.
Volume of a semi-sphere formula: V_semi-sphere = (2/3)πr^3
Calculate the volume of the semi-sphere:
V_semi-sphere = (2/3) * 3.14 * (14.5)^3
V_semi-sphere = (2/3) * 3.14 * 30119.875
V_semi-sphere = 63200.416 cubic feet
3. Total Volume = V_cylinder + V_semi-sphere
Total Volume = 22560.71 + 63200.416
Total Volume ≈ 85761 cubic feet
Therefore, the total volume of the shape is approximately 85761 cubic feet.