Question

Sally is filling glass containers in the shape of cylinders with different colors of sand. Each cylinder has a radius of 4 inches and a height of 8 inches. Part A. Sally has 1,000 cubic inches of sand. How many containers can she fill complelety? Your answer Part B. Sally says that if she finds cylindrical containers that have a radius and height half the height of the original containers, the volume of the new contianers would be half the volume of the original container. Is Sally correct? Use words, numbers, and/or symbols to support your answer. *

Answer 1

Part A.
We are given the total volume of the amount of sand she will want to fill
we are also given the shape and dimensions of the cylinders
Total volume of the sand = 1,000
Cylinder= radius 4 in, and height 8 in
the volume of a cylinder is V=πr^2h
We will solve for the volume of the cylinders
V=πr^2hV=π(4)^2*(10)
V = π (16) * (10)
V = π 160
The volume of the cylinders she wants to fill is 502.65 in^3
How many cylinders will she need
Well,
1000/502.65 ≈ 1.98
She will need two cylinder cans to fill with the 1,000 in^3 of sand

Part B.
To see if this is true, we find the half of the original cylinder's radius and height then solve for the volume and compare
V=πr^2h
The height and radius of the original cylinders were 4 r and 8h
we will find half of that which will be : 2 r and 4 h
Now solve for the volume V=πr^2h
V=π(2)^2* (4)
V=π (4)*(4)
V = π 16
V ≈ 50.26  inches ^3
The volume of the original cylinders was 502.65 in^3 and the volume of the new cylinders is 50.26 in^3...  Clearly the volume of the new cylinders is NOT half of the original. Sally is not correct!

Hope this helps :)