Question

Must answer correctly don't put something random for points or getting reported

You have recently purchased a new backpack as show in the picture. The main section of the backpack is made of a rectangle gular prism. Use the diagram to find the volume of your new backpack, then explain how u calculated the answer. Use the pictures with the formulas to help also use the sentence starters.
Sentence Starters:
The volume of the large rectangular prism (the bottom part of the backpack) is __inᶾ.
The volume of the pocket, which is also a rectangular prism is _____ inᶾ.
The volume of the half cylinder, which is the top curve of the backpack, is _____ inᶾ.
When you add all three of these together, you get the total volume of _____ inᶾ.

Hint: Find the volume of each shape; there are 3 of them; two rectangular prisms and half of a cylinder, and then add all 3 of them together. For the cylinder, you only need half, so find the volume of the whole cylinder then divide it by 2 for half. )

Answer 1

Main part of backpack V = 840 inᶾ

Front pocket of backpack V = 64 inᶾ

Top curve of the backpack V = 395.8406744 inᶾ

Total V = 1299.840674 inᶾ

Explanation:

1.

As we know, the formula for the volume of a rectangular prism is width x height x length (V = whl). We will use this formula to find the volume of the large rectangular prism (bottom part of the backpack) and the volume of the smaller rectangular prism (the pocket). As for the cylinder, we know the formula for the volume of a cylindrical prism is pi x radius squared x height (V = πr^2h). We will use this formula to find the volume of the half cylinder (top curve of the backpack).

2.

For the large rectangular prism (main part of the backpack), we are given:

w = 7in

h = 10in

l = 12in

Now let's incorporate our formula for the volume of a rectangular prism into this situation.

V = whl

V = 7 x 10 x 12

V = 840 inᶾ

3.

Now for the smaller rectangular prism (front pocket of backpack), we are given:

w = 2in

h = 4in

l = 8in

Now let's incorporate our formula for the volume of a rectangular prism into this situation.

V = whl

V = 2 x 4 x 8

V = 64 inᶾ

4.

Now to calculate volume for the half cylinder (top curve of the backpack), we must first imagine that this is a full, circular cylinder. We are given:

r = 6in

h (which will be the same as the width of the backpack in this case scenario) = 7in

Now let's incorporate our formula for the volume of a rectangular prism into this situation.

V* = πr^2h

V* = π x 6^2 x 7

V* = 791.6813487 inᶾ (round this number if you must)

Now that we have the volume of a whole cylinder, we can halve it (divide by two) since we only need half of the cylinder.

V = V*/2

V = 791.6813487/2

V = 395.8406744 inᶾ (round this number if you must)

5.

Finally, we can add our volumes together to acquire the volume of the backpack as a whole!

Large rectangular prism (bottom part of the backpack) + Smaller rectangular prism (the pocket) + Half cylinder (top curve of the backpack) = Total Volume (Whole backpack)

Recall that:

Large rectangular prism (bottom part of the backpack) = 840 inᶾ

Smaller rectangular prism (the pocket) = 64 inᶾ

Half cylinder (top curve of the backpack) = 395.8406744 inᶾ

So:

Total Volume (Whole backpack) = 840 inᶾ + 64 inᶾ + 395.8406744 inᶾ

Total Volume (Whole backpack) = 1299.840674 inᶾ (round this number if you must)