the diagram shows a composite solid consisting of cone and a hemisphere.the cone has a height of 10 cm a base diameter of 12 cm .Find volume. Of the whole solid.
the diameter of the hemisphere is the same as the base of the cone.
So, add up a cone and half of a sphere.
I trust that you have those formulas handy. Just plug in your numbers.
To find the volume of the whole solid, we need to find the individual volumes of the cone and the hemisphere, and then add them together.
Let's start with the cone:
The height of the cone is given as 10 cm, and the base diameter is given as 12 cm. The radius of the cone can be found by dividing the diameter by 2, so the radius of the cone is 12 cm / 2 = 6 cm.
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, π is approximately 3.14159, r is the radius, and h is the height.
Plugging in the values, the volume of the cone is V = (1/3) * 3.14159 * 6^2 * 10 = 376.991 cm^3 (rounded to 3 decimal places).
Now let's move on to the hemisphere:
Since the hemisphere is half of a sphere, we can use the formula for the volume of a sphere and divide it by 2.
The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume, π is approximately 3.14159, and r is the radius.
The radius of the hemisphere is the same as the radius of the cone, which is 6 cm.
Plugging in the values, the volume of the hemisphere is V = (4/3) * 3.14159 * 6^3 / 2 = 452.389 cm^3 (rounded to 3 decimal places).
Finally, we add the volumes of the cone and the hemisphere to get the volume of the whole solid:
Volume of whole solid = Volume of cone + Volume of hemisphere
Volume of whole solid = 376.991 cm^3 + 452.389 cm^3 = 829.380 cm^3 (rounded to 3 decimal places).
Therefore, the volume of the whole solid is approximately 829.380 cm^3.
To find the volume of the whole solid, we first need to find the volume of both the cone and the hemisphere separately, and then add them.
1. Volume of the Cone:
The formula for the volume of a cone is V_c = (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 base diameter is given as 12 cm, so the radius of the base (r) is half of that, i.e., 6 cm. And the height (h) is given as 10 cm.
Now, substituting the values into the formula:
V_c = (1/3) * π * (6 cm)^2 * 10 cm
V_c = (1/3) * π * 36 cm^2 * 10 cm
V_c = (1/3) * π * 360 cm^3
V_c ≈ 376.991 cm^3 (rounded to three decimal places)
2. Volume of the Hemisphere:
The formula for the volume of a hemisphere is V_h = (2/3) * π * r^3, where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is the same as the radius of the cone's base, which is 6 cm.
Now, substituting the values into the formula:
V_h = (2/3) * π * (6 cm)^3
V_h = (2/3) * π * 216 cm^3
V_h ≈ 452.389 cm^3 (rounded to three decimal places)
3. Volume of the Whole Solid:
To find the volume of the whole solid, we add the volumes of the cone and the hemisphere:
V_whole = V_c + V_h
V_whole ≈ 376.991 cm^3 + 452.389 cm^3
V_whole ≈ 829.380 cm^3 (rounded to three decimal places)
Therefore, the volume of the whole solid (consisting of the cone and the hemisphere) is approximately 829.380 cm^3.