Answered

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a circle with radius 12 mm is rotated around a diameter what is the volume of the solid formed

Sagot :

Volume of a sphere

We know that the radius of the sphere will be equal to the radius of the circle:

Since the equation for the volume of the sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

where r is the radius

r = 12 mm

and

π = 3.1416

We can replace it:

[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot(12\operatorname{mm})^3 \\ \downarrow\text{ since}(12\operatorname{mm})^3=1728\operatorname{mm}^3 \\ V=\frac{4}{3}\pi\cdot1728\operatorname{mm}^3 \\ \downarrow\text{ since }\frac{4}{3}\cdot1728=2304 \\ V=2304\pi\operatorname{mm}^3 \\ \downarrow\text{ since }\pi=3.1416 \\ V=7238.2\operatorname{mm}^3 \end{gathered}[/tex]

Answer

Then, the volume is given by

2304π mm³

or

7238.2 mm³

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