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WVU Math 129 & Math 155 Joint Warkbook 62 Math 129 Volume and Area Name: Volume

ID: 2910229 • Letter: W

Question

WVU Math 129 & Math 155 Joint Warkbook 62 Math 129 Volume and Area Name: Volume of a Box A box has the dimensions given in the diagram 2 ft Ift a) Find a formulh for the voume of gis in the tank shown as a finction of the depth Keep 1. 3 ft units (use 3ft, not 3) and frd the volme m term of gallons with 1,6-75gal b) What is the practical domain and range of your function? Express each in interval notation The practical domain and range deal with numbers that are realistic in a problem shuation) 6 c) Use the fornmula in part a) to find the total volkume in galons. Area of a Combined Shape 2. The region is composed of two simple shapes: A triangle with a base of 2ft and a height of 2and attached tothe base oftx tringle a rectangle 2,0 by ift, Find a formul forte area shown inchded up to x. Note that x can vary from the bottom of the triangle up to the top of the rectangle. (Hint: There will be two separate formulas depending on what value x has.) Ift M(x)- 2 ft Functions and Models 6-3

Explanation / Answer

a). Solution : We know that volume of cuboid = length x breath x height

Thus

V(x)= (3 ft)(2 ft) (x ft)

V(x)= 6x ft^3.

Since 1 ft^3 =7.5 gal.

Therefore

V(x) = 6*7.5 x gal

= 450x gal. Ans.

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b). For the domain, the value of should be greater than 0 and less than or equal to one for this problem i. e.

Domain (0, 1].

Range is (0, 450].

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c) For the total volume, x = 1.

Thus total volume = 450 gallons.

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2). Solution : Area = area of the rectangle + area of the triangle

Thus

A(x) = (2 ft)(1 ft) + 1/2 (x ft)(x ft)

=2 + (x^2 /2 ) ft^2. Ans