Rose Harrison and Clara Huizink Solutions for Exercise 11: Practice 4

The height of a cylinder is twice as long as its diameter. Its volume is $500 {\mathrm{cm}}^3$. Find the area of its base.

The diagonal of a cube (that passes through the middle of the cube, as shown in the diagram at right) measures $17.32 \mathrm{cm}$. Find the volume of the cube.

A box with no top has a height that is six times its length and a width that is $\frac{2}{3}$ of its height. If the surface area is $576 {\mathrm{cm}}^2$, find the dimensions of the box.

When milk freezes, its volume increases by one-fifteenth. Find the fraction by which its volume will decrease when it melts back into a liquid state.

It takes Nathan twice as long mow the lawn with the pushmower than with the electric mower. One day, he used the electric mower for $30$ minutes. Then it broke down. He took $20$ minutes the lawn with the pushmower finish mowing. Find how long it takes Nathan to mow the whole lawn using only the electric mower. 

The surface area of a cube-shaped box without a top is $252 {\mathrm{cm}}^2$. Find the volume of the box.

Suppose you have a $4\mathrm{L}$ container and a $9\mathrm{L}$ container. If you had access to a source of running water, explain how you could measure out exactly $6\mathrm{L}$ of water.