Volume of Cube

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?
 

Solved Problem 01 | Cube

Problem 01
Show that (a) the total surface of the cube is twice the square of its diagonal, (b) the volume of the cube is $\frac{1}{9}\sqrt{3}$ times the cube of its diagonal.
 

Solution 01
Space diagonal $s = a\sqrt{3}$, thus, $a = \dfrac{s}{\sqrt{3}}$
 

(a) Show that A = 2s2
$A = 6a^2$

$A = 6\left( \dfrac{s}{\sqrt{3}} \right)^2$

$A = 6\left( \dfrac{s^2}{3} \right)$

$A = 2s^2$       okay!
 

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