023 Review Problem - Lead pipe melt into a cube

Problem 23
It is desired to cut off a piece of lead pipe 2 in. in outside diameter and 1/4 in. thick, so that it will melt into a cube of edge 4 in. How long a piece will be required?

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
04-cube.jpgFind 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 ft3 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?


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