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Find the volume of this figure.

Find the volume of this figure.-example-1
User Quentin F
by
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1 Answer

9 votes
9 votes

Explanation:

2 basic objects are combined to this figure.

a prism or box of 20×8×18

a diagonally cut box (so, triangle shaped) of 8×18 base area and 10 being the triangle Hypotenuse.

the volume of the box is easy :

20×8×18 = 2,880

for the triangle-shaped half-box we need to get the height (the third leg of the side triangle).

we get this by Pythagoras

Hypotenuse² = leg1² + leg2²

10² = 8² + height²

100 = 64 = height²

36 = height²

height = 6

so, the area of a side triangle is

8×6/2 = 8×3 = 24

and the volume of the half-box is

24 × 18 = 432

so, the total volume of the figure is

2,880 + 432 = 3,312

User Adriano Castro
by
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