The question
Question: find the volume of a box 4 long, 3 wide and 2 high.
1 Length × width × height
Volume is how much space is inside.
We count the 1 by 1 by 1 cubes that fit.
The volume of a box is V = length × width × height.
V = length × width × height
Now put the numbers in: length = 4, width = 3 and height = 2.
V = 4 × 3 × 2
4 times 3 is 12.
That is one layer of 12 cubes.
There are 2 layers.
So V = 12 × 2.
V = 12 × 2
12 times 2 is 24.
So the volume is 24 cubic units.
V = 24
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The question
Question: find the surface area of a box 4 cm long, 3 cm wide and 2 cm high.
1 Count the faces
The surface area is the area of all the outside faces.
A box has 6 faces.
They come in 3 pairs, the same size.
2 Top and bottom
The top is 4 by 3.
Its area is 4 times 3, that is 12.
The bottom is the same.
Two faces of 12: 2 times 12 is 24.
2 × (4 × 3) = 2 × 12 = 24 cm2
3 Front and back
The front is 4 by 2.
Its area is 4 times 2, that is 8.
The face behind it is the same.
Two faces of 8: 2 times 8 is 16.
2 × (4 × 2) = 2 × 8 = 16 cm2
4 The two sides
The side is 3 by 2.
Its area is 3 times 2, that is 6.
The face behind it is the same.
Two faces of 6: 2 times 6 is 12.
2 × (3 × 2) = 2 × 6 = 12 cm2
5 Add all the faces
Add the three pairs: 24 + 16 + 12.
S = 24 + 16 + 12
24 plus 16 is 40.
S = 40 + 12
40 plus 12 is 52.
So the surface area is 52 cm².
S = 52 cm2
Let's look back.
First: count the faces.
Then: top and bottom.
Then: front and back.
Then: the two sides.
Last: add all the faces.
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The question
Question: find the volume of a cylinder with radius 5 and height 4.
1 Circle times height
The top is a circle.
Its area is π × r².
The cylinder is that circle, stacked up 4 high.
π is a special number for circles.
It is about 3.14.
So the volume is V = π × r² × h.
V = π × r2 × h
Now put the numbers in: r = 5 and h = 4.
V = π × 52 × 4
5² means 5 times 5.
That is 25.
52 = 5 × 5 = 25
So V = π × 25 × 4.
V = π × 25 × 4
25 times 4 is 100.
So V = 100π.
We keep π in the answer.
That is the exact answer.
V = 100π
2 About how much
To see about how much, put 3.14 for π.
V ≈ 100 × 3.14
100 times 3.14 is 314.
So the volume is about 314 cubic units.
V ≈ 314
Let's look back.
First: circle times height.
Last: about how much.
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