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andrew-mc [135]
3 years ago
12

A workbox has the following interior dimensions:

Mathematics
2 answers:
Elena-2011 [213]3 years ago
8 0
35 square inches. To find volume measure length by width by height
pav-90 [236]3 years ago
5 0

Answer:

the interior volume is 35 cubic inches

Step-by-step explanation:

Hello , I can help you with this.

to find the volume of the workbox you must multiply its dimensions,it is

Volume=length*width*height

also, you need convert the mixed number into fraction numbers

remember

a\frac{b}{c}=\frac{ac+b}{c}\\

Step 1

convert the mixed numbers into fraction numbers

length

4 inches=4 inches

width

2\frac{1}{2}\  inches= \frac{2*2+1}{2}\ inches=\frac{5}{2}\ inches \\

height

3\frac{1}{2}\  inches= \frac{3*2+1}{2}\ inches=\frac{7}{2}\ inches \\

Step 2

put the values into the equation

Volume=length*width*height

remember the unit( in)

Volume=\frac{4}{1} *\frac{5}{2}*\frac{7}{2}\\Volume= \frac{4*5*7}{1*2*2}\\ Volume=\frac{140}{4} \\Volume=35\\

in*in*in= cubic in

so, the interior volume is 35 cubic inches

have a nice day.

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Can someone help me with this?
yan [13]
I'm assuming you want the total surface area.

This is a trapezoidal prism. The bases are the parallel faces running horizontal (parallel to the ground) and they are congruent trapezoids. The lateral sides are rectangles.

-------------------------------------------------

Lateral Faces:
The back face (hidden from view) is a rectangle that is 12 inches by 3 inches, so it has an area of 12*3 = 36 sq inches

The front slant faces on the left and right are each 3*5 = 15 sq inches in area

The front center lateral face has area of 6*3 = 18 sq inches

The total lateral surface area is 15+18+15+36 = 84 sq inches

-------------------------------------------------

The bases are each the same trapezoid. The trapezoid has two parallel sides of 12 and 6 inches. Call this b1 and b2. The height of the trapezoid is h = 4. Imagine the trapezoid is laid flat in a 2D perspective instead of a 3D one.

The area of one trapezoid is...
A = h*(b1+b2)/2
A = 4*(12+6)/2
A = 4*(18)/2
A = 72/2
A = 36

So the area of both base faces combined is 2*36 = 72

-------------------------------------------------

The total surface area is then found by adding the total lateral surface area (84) and the total base area (72) to get 84+72 = 156

Final Answer: 156 square inches

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