Volume of Cones, Cylinders, and Spheres Quick Check
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Question
Use the image to answer the question.
A hemisphere is placed on top of an inverted cone. The back of the circumference, the radius, and the perpendicular height of the cone are marked with dashed lines. The radius and the height make a right angle and are perpendicular.
An engineer wants to know the volume of the following object composed of a hemisphere and a cone. She knows the height of the cone is equal to the diameter of the hemisphere, and the volume of the cone is 12 m3 . What is the volume of the whole object?(1 point)
Responses
18 m3
18 m cubed
36 m3
36 m cubed
There is not enough information to say.
There is not enough information to say.
24 m3
24 m cubed
1=cone ect.
2=24
3=50/3
4=36
5=24
i got answers you want
To find the volume of the whole object, we need to find the volume of both the hemisphere and the cone and add them together.
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is 12 m^3, we can substitute the values into the formula: 12 = (1/3)πr^2h.
Since the height of the cone is equal to the diameter of the hemisphere, we can write h = 2r.
Substituting this into the volume formula: 12 = (1/3)πr^2(2r).
Simplifying, we get 12 = (2/3)πr^3.
Multiplying both sides by 3/2π, we get 18 = r^3.
Taking the cube root of both sides, we get r = 3.
Now that we have the radius of the cone, we can find the volume of the hemisphere. The volume of a hemisphere is given by the formula V = (2/3)πr^3.
Substituting r = 3 into the formula, we get V = (2/3)π(3)^3 = 54π.
Adding the volume of the cone (12 m^3) to the volume of the hemisphere (54π m^3), we get the volume of the whole object as 12 + 54π m^3.
Since we do not have the exact value of π, we can leave the answer in terms of π or approximate it using a calculator.
pick a naswer choicw
The volume of the whole object is:
24 m3
24 m cubed
To find the volume of the entire object composed of a hemisphere and a cone, we first need to find the volume of the hemisphere and the volume of the cone separately.
The volume of a hemisphere is given by the formula: V = 2/3 * π * r^3, where r is the radius of the hemisphere.
The volume of a cone is given by the formula: V = 1/3 * π * r^2 * h, where r is the radius of the base and h is the height of the cone.
In this case, the height of the cone is given as the diameter of the hemisphere, which means the height of the cone is equal to 2 times the radius of the hemisphere.
Given that the volume of the cone is 12 m^3, we can substitute the formula for the cone volume and solve for the radius:
12 = 1/3 * π * r^2 * 2r
12 = 2/3 * π * r^3
18 = π * r^3
r^3 = 18 / π
r ≈ 2.72 (rounded to two decimal places)
Now that we have the radius of the hemisphere (which is also the diameter of the base of the cone), we can find the volume of the hemisphere using the hemisphere volume formula:
V_hemisphere = 2/3 * π * (2.72)^3
V_hemisphere ≈ 31.43 (rounded to two decimal places)
To find the volume of the entire object, we need to add the volume of the hemisphere and the volume of the cone together:
V_object = V_hemisphere + V_cone
V_object ≈ 31.43 + 12
V_object ≈ 43.43 (rounded to two decimal places)
Therefore, the volume of the whole object is approximately 43.43 m^3. So the correct response is:
43 m^3