Answer:
78 ft³
Step-by-step explanation:
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Volume of a rectangular prism = length × width × height
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<u>Toy Box</u>
- length = 5 ft
- width = 3 ft
- height = 2ft
⇒ volume = 5 × 3 × 2 = 30 ft³
<u>Book Box</u>
- length = 6 ft
- width = 4 ft
- height = 2 ft
⇒ volume = 6 × 4 × 2 = 48 ft³
Total combined volume = 30 + 48 = 78 ft³
Is there supposed to be a picture??!
Answers:
- a) 693 sq cm (approximate)
- b) 48 sq cm (exact)
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Explanation:
Part (a)
A regular triangular pyramid, aka regular tetrahedron, has all four triangles that are identical copies of one another. They are congruent triangles. This will apply to part (b) as well.
To find the area of one of the triangles, we'll use the formula
A = 0.25*sqrt(3)*x^2
where x is the side length. This formula applies to equilateral triangles only.
In this case, x = 20, so
A = 0.25*sqrt(3)*x^2
A = 0.25*sqrt(3)*20^2
A = 173.20508 approximately
That's the area of one triangle, but there are four total, so the entire area is about 4*173.20508 = 692.82032 which rounds to 693 sq cm.
The units "sq cm" can be written as "cm^2".
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Part (b)
We'll use the same idea as part (a). But the formula to find the area of one triangle is much simpler.
The area of one of the triangles is A = 0.5*base*height = 0.5*6*4 = 12 sq cm.
So the area of all four triangles combined is 4*12 = 48 sq cm
This area is exact.
The area of each 2D flat net corresponds exactly to the surface area of each 3D pyramid. This is because we can cut the figure out and fold along the lines to form the 3D shapes.
For 24 keep the orders of operation in mind. So first we'd work out what's in parentheses, so we'd start by doing 5-3, which is 2. We'd then add 2+2 to get 4. Then we multiply 16 and 4 to get 64. So the correct answer is 64.
For the second part of 24 we first multiply 3 and 4 to get 9. We would then subtract 17-9 to get 8. Finally, we'd add 8+2 to get 10. So the correct answer is 10.
As for 25, the answer is 6400 centimeters^3.
