Question

PLS HELP ME!!! The figure is made up of a cone and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box. cm³

Answer 1

Hello!

The figure is made up of a cone and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π . Enter your answer in the box. cm³

Data: (Cone)

h (height) = 12 cm

r (radius) = 4 cm (The diameter is 8 being twice the radius)

Adopting: $\pi \approx 3.14$

V (volume) = ?

Solving: (Cone volume)

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

$V = \dfrac{ 3.14 *4^2*\diagup\!\!\!\!\!12^4}{\diagup\!\!\!\!3}$

$V = 3.14*16*4$

$\boxed{V = 200.96\:cm^3}$

Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

r (radius) = 4 cm

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:

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

$V = 2*3.14 * \dfrac{4^3}{3}$

$V = 2*3.14 * \dfrac{64}{3}$

$V = \dfrac{401.92}{3}$

$\boxed{ V_{hemisphere} \approx 133.97\:cm^3}$

What is the approximate volume of this figure?

Now, to find the total volume of the figure, add the values: (cone volume + hemisphere volume)

Volume of the figure = cone volume + hemisphere volume

Volume of the figure = 200.96 cm³ + 133.97 cm³

$\boxed{\boxed{\boxed{V = 334.93\:cm^3 \to Volume\:of\:the\:figure \approx 335\:cm^3 }}}\end{array}}\qquad\quad\checkmark$

Answer:

The volume of the figure is approximately 335 cm³

_______________________

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

Answer 2

The total volume of the figure is 603 cubic centimeters.

The figure is consists of the cone and the hemisphere in which dimensions of the figure are given.

The diameter of the hemisphere and the cone is 8 cm.

The height of the cone is 12 cm.

We need to determine the volume of the given figure.

The volume of the given figure is the addition of the volume of the cone and the hemisphere.

Thus,

$\rm{Total\;Volume}=Volume\; of\; Cone +Volume\;of\; Hemisphere$

Calculate the volume of cone and hemisphere separately and add up for the final result.

$\begin{aligned}\rm{Volume \;of\; cone}&=\dfrac{1}{3} \pi r^2h\\&= \dfrac{1}{3} \times3.14 \times4^2\times12\\&=200.96\end{aligned}$

$\begin{aligned}\rm{Volume \;of\; hemisphere}&=2 \pi r^3\\&= 2 \times3.14 \times4^3\\&=401.92\end{aligned}$

$\begin{aligned}\rm{Total\;Volume}&=200.96+401.92\\&=602.88\\&=603\;\rm{cm^3} \end{aligned}$

Thus, the total volume of the figure is 603 cubic centimeters.

To know more about the volume, please refer to the link:

https://brainly.com/question/23409099