Can anyone help me on few of these problems on on this Measuring Area & Volume study guide?

Question

1. A cube has a volume of 6 cubic centimeters. If all side lengths are doubled,what is the volume of the new cube?

3. The dimensions of a large cube are three times the dimensions of a small cube. What could be the volumes of the two cubes?

6. A cylinder has a volume of 81π cubic cm. What is the volume of a cone with the same base and height as this cylinder?

Answer 1

1 - Since it's a cube, we know that V = s³ and, in this case, V = 6 cm³ = s³. 

Now if the sides are doubled, then the new volume would be V₂ = (2s)^{3 =} 2³s³ =8s³.

Since s³ = 6 cm³, then V₂ = 8(6 cm³) = 48 cm³

3. Not sure if something is missing from this, but... If the large cube dimensions are three times that of a small cube, then similar to #1, V₂ = (3s)³ = 27s³ - so the Volume of the large cube would be 27 times that of the small cube. 

6. Volume of a cylinder is ∏r²h. Volume of a cone is 1/3 ∏r²h. if the base and the height are the same, then cone would have a volume of 1/3 of the cylinder, or 27∏ cm³