the diameter of a sphere is 16 cm what is the sphere's volume? round to the nearest tenth
The radius of a sphere can be found by dividing the diameter by 2:
radius = diameter/2 = 16 cm/2 = 8 cm
The volume of a sphere can be found using the formula:
volume = (4/3) * π * radius^3
Plugging in the values:
volume = (4/3) * 3.14 * (8 cm)^3
Simplifying:
volume = (4/3) * 3.14 * 512 cm^3
volume = 2143.56 cm^3
Rounding to the nearest tenth:
volume ≈ 2143.6 cm^3
Therefore, the sphere's volume is approximately 2143.6 cm^3.
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Question
Oatmeal is packaged in a cylindrical container, as shown in the diagram. The diameter of the container is 13 centimeters and its height is 24 centimeters. To the nearest tenth of a cubic centimeter, what is the volume of the container?
Responses
A 3,185.6 cubic centimeters3,185.6 cubic centimeters
B 3,256.2 cubic centimeters3,256.2 cubic centimeters
C 3,325.7 cubic centimeters3,325.7 cubic centimeters
D 3,855.3 cubic centimeters
The formula for the volume of a cylinder is V = π * r^2 * h, where r is the radius of the base and h is the height.
Given that the diameter of the container is 13 cm, the radius would be half of that, which is 6.5 cm.
Plugging the values into the formula:
V = 3.14 * (6.5 cm)^2 * 24 cm
V ≈ 3.14 * 42.25 cm^2 * 24 cm
V ≈ 3.14 * 1014 cm^3
V ≈ 3186.36 cm^3
Rounded to the nearest tenth of a cubic centimeter, the volume of the container is approximately 3186.4 cubic centimeters.
Therefore, the correct response is A) 3,185.6 cubic centimeters.
Find the volume of a cylinder if it has a diameter of 8 and a height of 12. Leave your answer in terms of π.
Responses
A 64π64π
B 192π192π
C 256π256π
D 768π
The formula for the volume of a cylinder is V = π * r^2 * h, where r is the radius and h is the height.
Given that the diameter of the cylinder is 8, the radius would be half of that, which is 4.
Plugging the values into the formula:
V = π * (4)^2 * 12
V = π * 16 * 12
V = π * 192
So, the volume of the cylinder is 192π.
Therefore, the correct response is B) 192π.