Question

Calculate the volume of each solid. 14 cm 18 cm 22 cm 19 cm

Answer 1

9514 1404 393

Answer:

  10,450 cm³

Step-by-step explanation:

The volume is the product of the area of the facing face and the depth of the figure. The area of the facing face is the sum of the areas of a rectangle and a triangle. The relevant area formulas are ...

  A = bh . . . . . area of rectangle with base b and height h

  A = 1/2bh . . . area of triangle with base b and height h

Here the rectangle and triangle have the same base, 19 cm. Then the sum of the areas is ...

  Atot = (19 cm)(18 cm) + 1/2(19 cm)(14 cm)

  Atot = (19 cm)(18 cm +1/2×14 cm) = (19 cm)(25 cm) = 475 cm².

Then the volume of the figure is ...

  V = Bh = (475 cm²)(22 cm) = 10,450 cm³

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Additional comment

Effectively, this is the volume of a cuboid whose height is that of the bottom rectangular prism (18 cm) plus half the height of the triangular prism on top (1/2×14 cm = 7 cm). (18+7=25) The volume is essentially 19 cm × 25 cm × 22 cm. This recognition can serve to simplify the work or to act as a check on the work done some other way.