Mathematics, 05.07.2019 05:30 graciewyatt6833

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. find the volume in terms of p

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Answer from: s108870

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!

Answer from: kklove6700

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: $\pi \approx 3.14$

V (volume) = ?

Solving: (Cylinder volume)

$V = \pi *r^2*h$

V = 3.14 *3^2*12

V = 3.14*9*12

$\boxed{V_{cylinder} = 339.12\:in^3}$

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: $\pi \approx 3.14$

If: We know that the volume of a sphere is $V = 4* \pi * \dfrac{r^3}{3}$ , but we have a hemisphere, so the formula will be half the volume of the hemisphere $V = \dfrac{1}{2}* 4* \pi * \dfrac{r^3}{3} \to \boxed{V = 2* \pi * \dfrac{r^3}{3}}$

Formula: (Volume of the hemisphere)

$V = 2* \pi * \dfrac{r^3}{3}$

Solving:

$V = 2* \pi * \dfrac{r^3}{3}$

$V = 2*3.14 * \dfrac{3^3}{3}$

$V = 2*3.14 * \dfrac{27}{3}$

V = 2*3.14*9

$\boxed{ V_{hemisphere} = 56.52\:in^3}$

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

$\boxed{\boxed{\boxed{Volume\:of\:the\:figure = 395.64\:in^3}}}\end{array}}\qquad\quad\checkmark$

_______________________

I Hope this helps, greetings ... Dexteright02! =)

Find the volume of the figure if the radius of the hemisphere and cylinder is 6 inches and the heigh

Answer from: Quest

i think it's either c or d

step-by-step explanation: the entire question is extremely odd. 04 obviously refers to the interest rate. honestly i will say the answer is c. because the (2 x 12) part would mean it's compounded semiannually. i'll say choose c.

Someone i retook this test twice already

Answer from: Quest

if you explain the the question more correctly i might be able to answer this better

step-by-step explanation:

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Find the volume of the figure if the radius of the hemisphere and cylinder is 6 inches and the heigh...