A farmer's cylindrical silo has a radius of 2 m and is filled with grain to a height of 10 m.
He is using the grain to fill bags that are 40 cm by 40 cm by 80 cm. How many bags will he be able to fill?
a 1012 b. 982
c. 1049 d. 859
The volume of the silo can be calculated using the formula for the volume of a cylinder, which is given by V = πr^2h, where r is the radius and h is the height.
In this case, the radius is 2 m and the height is 10 m, so the volume of the silo is V = π(2^2)(10) = 40π cubic meters.
The volume of each bag can be calculated using the formula for the volume of a rectangular prism, which is given by V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length, width, and height are all given in centimeters, so we need to convert them to meters. There are 100 centimeters in a meter, so the volume of each bag is V = (40/100)(40/100)(80/100) = 0.32 cubic meters.
To find the number of bags that can be filled, we divide the volume of the silo by the volume of each bag:
Number of bags = (40π) / 0.32 = 125π ≈ 392.699
Rounded to the nearest whole number, the farmer will be able to fill approximately 393 bags.
Therefore, the correct answer is not among the options provided.