# Solved Problem 10 | Cube

**Problem 10**

Pass a plane through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section.

# Solved Problem 09 | Cube

**Problem 09**

One cube has a face equivalent to the total area of another

cube. Find the ratio of their volumes.

# Solved Problem 08 | Cube

**Problem 08**

If a cube has an edge equal to the diagonal of another cube, find the ratio of their volumes.

# Solved Problem 07 | Cube

**Problem 07**

Find the area of the triangle whose vertex is at the midpoint of an upper edge of a cube of edge a and whose base coincides with the diagonally opposite edge of the cube.

# Solved Problem 06 | Cube

**Problem 06**

The plane section ABCD shown in the figure is cut from a cube of edge a. Find the area of the section if D and C are each at the midpoint of an edge.

# Solved Problem 05 | Cube

**Problem 05**

A vegetable bin built in the form of a cube with an edge of 6 ft. is divided by a vertical partition which passes through two diagonally opposite edges. Find the lateral surface of either compartment.

# Solved Problem 04 | Cube

**Problem 04**

Find the volume and total area of the largest cube of wood that can be cut from a log of circular cross section whose radius is 12.7 inches. See figure.

# Solved Problem 03 | Cube

**Problem 03**

What is the weight of a block of ice 24 in. by 24 in. by 24 in., if ice weighs 92 per cent as much as water, and water weighs 62.5 lb per cu. ft.?

**Solution 03**

Unit weight of water

$\gamma_{water} = 62.5 \, \text{ lb/ft}^3$

Unit weight of ice

$\gamma_{ice} = 92\% \, \gamma_{water}$

$\gamma_{ice} = 0.92(62.5)$

$\gamma_{ice} = 57.5 \, \text{ lb/ft}^3$

Volume of ice block

$V_{ice} = (24/12)^3$

$V_{ice} = 8 \, \text{ ft}^3$

Weight of 8 ft^{3} ice block

# Solved Problem 02 | Cube

**Problem 02**

How much material was used in the manufacture of 24,000 celluloid dice, if each die has an edge of 1/4 inch?