Problem 17

A painter is to cover the walls in a room that is 8.0 ft high and 12.0 ft along a side. What surface area (in square meters) must she cover?

SOLUTION:

First, we must find the area of the room. The room would have four such walls so we find the area of one wall and multiply it by 4.

A = (8.0 ft)(12.0 ft) = 96 ft²

Total area = 4A = 4(96 ft²) = 384 ft²

Now that we have the area in square feet, we must convert it to square meters.

Conversion factor: 1 m = 3.281 ft

384ft²(1m/3.281 ft) (1 m/3.281 ft) = 35.67 m²=36m²

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Problem 22

The base of a pyramid covers an area of 13.0 acres (1 acre = 43,560 ft²) and has a height of 481 ft. If the volume of the pyramid is given by the expression V = (1/3) bh, where b is the base and h is the height, find the volume of the pyramid in cubic meters.

SOLUTION:

You can convert everything to meters first or calculate the volume in cubic feet then convert to meters. Let’s do it the first way, by converting everything into meters first.

Conversion factor: 1 m = 3.281 ft

13.0acres = 13.0 (43,560 ft²) = 566,280 ft²(1m/3.281ft) (1m/3.281 ft) = 52603.999 m²

481ft = (481 ft)(1m/3.281 ft) = 146.6 m

V= (1/3)bh = (1/3)(52603.999 m²)(146.6 m) = 2570610.9 m³(but check sig. Fig)

V=2.57 x 10⁶m³

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Problem 29

A point located in polar coordinates is given by r = 2.5 m andq= 35⁰.Find the x and y coordinates of this coordinate assuming the two coordinate systems have the same origin.

SOLUTION:

The equations of conversion are given by the following:

x= r cosq

y= r sinq

So, we just plug in the appropriate numbers in to the equations:

x= (2.5 m) cos(35⁰) = 2.05 m =2.1 m

y= (2.5 m) sin(35⁰) = 1.43 m =1.4 m

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Problem 32

Two points in a rectangular coordinate system have coordinates (5.0, 3.0) and (-3.0, 4.0), where the units are centimeters. Determine the distance between these points.

SOLUTION:

The equation below is used to find the distance between two coordinates:

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