Problem 1

A shape that covers an area A and has a uniform height h has a volume given by V = Ah.

(a) Show that V = Ah is dimensionally correct.

SOLUTION:

The volume has dimensions of length cubed or: L³

Area has dimensions of length squared or: L²

The height has dimensions of length or: L

V = Ah

L³ = (L²)(L) = L³ therefore the formula is dimensionally correct.

(b) Show that the volumes of a cylinder and of a rectangular box can be written in the form V = Ah and identify the A in each case.

SOLUTION:

The volume of a cylinder V = pr² h where the A = pr² = the area of the circular face of the cylinder.

The volume of a rectangular box V = l x w x h where l = length, w = width, and h = height. Recall that the area of a rectangle A = l x w, so V = Ah.

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Problem 6

The value of the speed of light is known to be 2.99792458 x 10⁸ m/s. Express the speed of light to

(a) three significant figures

ANSWER:

3.00 X 10⁸ m/s

(b) five significant figures

ANSWER:

2.9979 x 10⁸ m/s

(c) seven significant figures

ANSWER:

2.997925 x 10⁸ m/s

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Problem 8

Carry out the following arithmetic operations:

(a) 756 + 37.2 + 0.83 + 2.5 = 797

(b) 3.2 x 3.563 = 11

(c) 5.67 x p = 17.8

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Problem 14

Estimate the age of the Earth in years, using the data in Table 1.3 and the appropriate conversion factors.

SOLUTION:

Age of the Earth = (1 x 10¹⁷ s) X (1 year/3 x 10⁷ s) = 3 x 10⁹ years.

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