Question

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.
Which expression represents the volume, in cubic units, of the shaded region of the composite figure?

One-half(14)(10)(8) – π(2.52)(8)
One-half(14)(10)(8) + π(2.52)(8)
One-third (one-half)(10)(8)(14) – π(2.52)(8)
One-third (one-half)(10)(8)(14) + π(2.52)(8)

Answer 1

The expression that represents the volume, in cubic units, of the shaded region of the composite figure is option: A. One-half(14)(10)(8) – π(2.52)(8).

How to find the volume of a prism?

If the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base,

then its volume is:

V = B x  h

where h is the height of that prism and B is the area of the base of that prism.

Given:

Base side length =14 and 10 units

Height=8 units

Diameter=5 units

The volume of the shaded region is;

Expression =  1-( half 14)(10)(8) - π(2.52)(8)

Expression = 1-(7) (10)(8) - π(2.52)(8)

Expression = 1- (560)- 63.33

Expression = -559-63.33

Expression = -622.33

Hence, The expression that represents the volume, in cubic units, of the shaded region of the composite figure is option: A. One-half(14)(10)(8) – π(2.52)(8).

Learn more about volume of a prism here:

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