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 plug in the values and solve for the radius (r) and height (h) of the cone.
12 = (1/3)πr^2h
Since the height (h) is equal to the diameter of the hemisphere, which is twice the radius (2r), we can substitute h with 2r in the equation.
12 = (1/3)πr^2(2r)
Simplifying the equation:
12 = (2/3)πr^3
Multiplying both sides by 3/2π:
18 = r^3
Taking the cube root of both sides:
r = 3
Now that we have the radius (r), we can find the height (h) using h = 2r:
h = 2(3) = 6
Now, let's find the volume of the hemisphere. The volume of a hemisphere is given by the formula V = (2/3)πr^3.
V_hemisphere = (2/3)π(3^3) = (2/3)π27 = 18π
Finally, to find the volume of the whole object, we add the volume of the hemisphere to the volume of the cone:
V_total = V_hemisphere + V_cone
V_total = 18π + 12
Since the exact value of π is not given, we can approximate it as 3.14:
V_total ≈ 18(3.14) + 12 = 56.52 + 12
Therefore, the volume of the whole object is approximately 68.52 m^3.
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
24 m3
24 m cubed
18 m3
18 m cubed
36 m3
36 m cubed
There is not enough information to say.
1 answer