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 6-3Explanation / 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.
-----------------------------------
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].
---------------------------------
c) For the total volume, x = 1.
Thus total volume = 450 gallons.
--------------------------------------------------
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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.