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arlik [135]
2 years ago
12

Draw an example of a composite figure that has a volume between 750 cubic inches and 900 cubic inches

Mathematics
1 answer:
grigory [225]2 years ago
4 0

Volume:

V \approx 888.02in^3 \\ \\ And, \ 750in^3

<h2>Explanation:</h2>

A composite figure is formed by two or more basic figures or shapes. In this problem, we have a composite figure formed by a cylinder and a hemisphere as shown in the figure below, so the volume of this shape as a whole is the sum of the volume of the cylinder and the hemisphere:

V_{total}=V_{cylinder}+V_{hemisphere} \\ \\ \\ V_{total}=V \\ \\ V_{cylinder}=V_{c} \\ \\ V_{hemisphere}=V_{h}

So:

V_{c}=\pi r^2h \\ \\ r:radius \\ \\ h:height

From the figure the radius of the hemisphere is the same radius of the cylinder and equals:

r=\frac{8}{2}=4in

And the height of the cylinder is:

h=15in

So:

V_{c}=\pi r^2h \\ \\ V_{c}=\pi (4)^2(15) \\ \\ V_{c}=240\pi in^3

The volume of a hemisphere is half the volume of a sphere, hence:

V_{h}=\frac{1}{2}\left(\frac{4}{3} \pi r^3\right) \\ \\ V_{h}=\frac{1}{2}\left(\frac{4}{3} \pi (4)^3\right) \\ \\ V_{h}=\frac{128}{3}\pi in^3

Finally, the volume of the composite figure is:

V=240\pi+\frac{128}{3}\pi \\ \\ V=\frac{848}{3}\pi in^3 \\ \\ \\ V \approx 888.02in^3 \\ \\ And, \ 750in^3

<h2>Learn more:</h2>

Volume of cone: brainly.com/question/4383003

#LearnWithBrainly

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