Answer:
1) The volume of a hemisphere of radius R is equal to half the volume of a sphere of radius R.
Where the volume of a sphere of radius R is:
V = (4/3)*pi*R^3
In this case, the radius is R = 10ft
And pi = 3.14
2) Now we can just solve that equation to get:
V = (1/2)*(4/3)*3.14*(10ft)^3 = 2,093.33 ft^3
Where the (1/2) comes because the volume of the hemisphere is half the volume of a complete sphere, as we already said above.
4) We know that the volume of a cylinder is:
V = pi*(r^2)*h
where:
pi = 3.14
r represents the radius. The radius of the cylinder will be the same as the radius of the hemisphere, then r = 10ft
h is the height of the cylinder, in this case, h = 30ft
Then the volume is:
V = 3.14*(10ft)^2*(30ft) = 9,420 ft^3
The total volume is equal to the sum between the volumes of the cylinder and the volume of the hemisphere.
Then the total volume is:
Volume = 9,420 ft^3 + 2,093.33 ft^3 = 11,513.33 ft^3
Answer:
1. How can you find the volume of a hemisphere?
The volume of a hemisphere is half the volume of a sphere. The volume of a sphere is equal to V = (4/3)*pi*R^3
2. What is the volume of the hemisphere? Show your work.
V = (4/3)*pi*R^3
We can substitute pi for 3.14 and R for 10, and since we are finding the volume of a hemisphere, we divide by 2.
V = (1/2)*(4/3)*3.14*(10ft)^3
V = (1/2)*(4/3)*3.14*(10ft)^3 = 2,093.33 ft^3
3. What is the volume of the cylinder? Show your work.
The volume of the cylinder is 9,420ft^3
3.14*(10^2)*30=9,420
4. What is the total volume of the grain silo? Explain how you found your answer.
The total volume is 11,513.33 ft^3.
9,420 ft^3 + 2,093.33 ft^3 = 11,513.33 ft^3
