A grain silo is shaped like a cylinder with a height of 24 feet and a diameter of 10 feet. A farmer wishes to determine how many cubic feet of grain could fit in the silo. What is the maximum amount of cubic feet of grain that the silo could hold?
Answers
Here, we have to determine the cubic ft.of grain that could fit in the silo .....this means we have to calculate the volume of the silo.
h=24feet
d=10ft
r=d/2=5ft
now, volume of cylinder (v)=πr^2h
=> v= 5×5×24×π
=25×24×π
=5000π
=5000×3.141
=15705 cubic feet.
Answer:
Step-by-step explanation:
The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed (a cylinder and two cones). The silo is made up of a cylinder (with height 10 feet and base radius 5 feet) and two cones (each with height 5 ft and base radius 5 ft). The formulas given at the beginning of the SAT Math section:
Volume of a Cone
V=
1
3
πr2h
Volume of a Cylinder
V=πr2h
can be used to determine the total volume of the silo. Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is given by
Vsilo=π(52)(10)+(2)(
1
3
)π(52)(5)=(
4
3
)(250)π
which is approximately equal to 1,047.2 cubic feet.