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2 years ago

What is the volume of the shaded portion of the composite figure? Express your answer in terms of π.

Mathematics

2 answers:

Lerok [7]2 years ago

5 0

Answer:

Step-by-step explanation:

aleksley [76]2 years ago

3 0

we know that

The volume of the shaded portion of the composite figure is equal to the volume of a rectangular pyramid minus the volume of a cone

Step $1$

Find the volume of a cone

volume of the cone is equal to

$Vc=\frac{1}{3}* \pi* r^{2}*h$

where

r is the radius of the cone

h is the height of the cone

in this problem

$r=4.5\ units\\ h=12\ units$

Substitute in the formula above

$Vc=\frac{1}{3} \pi*4.5^{2}*12$

$Vc=81\pi \ units^{3}$

Step $2$

Find the volume of a rectangular pyramid

Volume of a rectangular pyramid is equal to

$Vp=\frac{1}{3}*B*h$

where

B is the area of the base

h is the height of the pyramid

in this problem

$B=10*15=150\ units^{2} \\ h=12\ units$

Substitute in the formula above

$Vp=\frac{1}{3}*150*12=600\ units^{3}$

Step $3$

Find the volume of the shaded portion of the composite figure

$Vp-Vc=(600-81\pi)\ units ^{3}$

therefore

the answer is

Find the volume of the shaded portion of the composite figure is

$(600-81\pi)\ units ^{3}$

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Answer:

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In Trapezoid is it not necessary that the diagonals bisect at all the cases
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Diagonals of rectangles must bisect each other
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