Examkin

Question

Difficulty: MediumVolume and Surface Area of 3D Figures

A farmer needs to completely fill a cylindrical grain silo with wheat. If the silo has a diameter of 1212 meters and a height of 1010 meters, what is the maximum capacity of the silo in cubic meters?

  1. A
    60π60\pi
  2. B
    120π120\pi
  3. 360π360\piAnswer
  4. D
    1440π1440\pi

Answer

The maximum capacity of the silo is 360π360\pi cubic meters.
The question asks for the maximum capacity to completely fill the silo, which means finding its volume. The volume of a cylinder is found using the formula V=πr2hV = \pi r^2 h. First, the diameter of 1212 meters must be halved to find the radius of 66 meters. Substituting the radius and the height (1010 meters) into the formula gives V=π(6)2(10)=π(36)(10)=360πV = \pi(6)^2(10) = \pi(36)(10) = 360\pi cubic meters.

Step-by-Step Solution

1
Determine the required measurement and the appropriate formula.
The problem asks for the capacity to 'fill' a cylinder, which requires the volume formula: V=πr2hV = \pi r^2 h.
Capacity refers to the interior space (volume) of a 3D figure.
2
Find the radius of the circular base.
The radius is half of the diameter: 12÷2=612 \div 2 = 6 meters.
The volume formula requires the radius, but the problem provides the diameter.
3
Substitute the values into the formula and solve.
V=π(6)2(10)=π(36)(10)=360πV = \pi(6)^2(10) = \pi(36)(10) = 360\pi cubic meters.
Executing the calculation according to the order of operations yields the final volume.

Key Concept

Volume of a Cylinder
Estimated Time:1m 0s
Rate this question

Topics

Volume and Surface Area of 3D Figures

More questions from this topic