Hello!
Find the volume of the figure if the radius of the hemisphere and cylinder is 6 inches and the height of the cylinder is 12 inches.
Data: (Cylinder)
h (height) = 12 in
r (radius) = 3 in (The diameter is 6 being twice the radius)
Adopting: [tex]\pi \approx 3.14[/tex]
V (volume) = ?
Solving: (Cylinder volume)
[tex]V = \pi *r^2*h[/tex]
[tex]V = 3.14 *3^2*12[/tex]
[tex]V = 3.14*9*12[/tex]
[tex]\boxed{V_{cylinder} = 339.12\:in^3}[/tex]
Note: Now, let's find the volume of a hemisphere.
Data: (hemisphere volume)
V (volume) = ?
r (radius) = 3 in (The diameter is 6 being twice the radius)
Adopting: [tex]\pi \approx 3.14[/tex]
If: We know that the volume of a sphere is [tex]V = 4* \pi * \dfrac{r^3}{3}[/tex] , but we have a hemisphere, so the formula will be half the volume of the hemisphere [tex]V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}[/tex]
Formula: (Volume of the hemisphere)
[tex]V = 2* \pi * \dfrac{r^3}{3}[/tex]
Solving:
[tex]V = 2* \pi * \dfrac{r^3}{3}[/tex]
[tex]V = 2*3.14 * \dfrac{3^3}{3}[/tex]
[tex]V = 2*3.14 * \dfrac{27}{3}[/tex]
[tex]V = 2*3.14*9[/tex]
[tex]\boxed{ V_{hemisphere} = 56.52\:in^3}[/tex]
Now, to find the total volume of the figure, add the values: (cylinder volume + hemisphere volume)
Volume of the figure = cylinder volume + hemisphere volume
Volume of the figure = 339.12 in³ + 56.52 in³
[tex]\boxed{\boxed{\boxed{Volume\:of\:the\:figure = 395.64\:in^3}}}\end{array}}\qquad\quad\checkmark[/tex]
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I Hope this helps, greetings ... Dexteright02! =)
Answer:
576 π
Step-by-step explanation:
You must split the shape into a cylinder and hemisphere.
Formula for a cylinder: πr^2h
The radius is 6 in. and the height is 12 in., and since you are solving in terms if π, your answer for the cylinder is 432 π.
Formula for a hemi-sphere: (4/3 πr^3) /2
The radius, again, is 6 in., so when you plug in the formula in terms if π, you get 144 π.
You add the two volumes together and your answer is 576 π.
Hope this helps!
