Please help me asap in this!!!!

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

899 round to the nearest ten

algol [13]

900 because 9 is greater than 5 so it rounds to my answer.

6 0

2 years ago

Read 2 more answers

Marguerite is building a box from strips of wood.she needs 78 pieces of wood that are each 29 centimeters long.the wood comes in

dolphi86 [110]

Each strip is 29 cm

------------------------------------------------------
Change the m to cm
------------------------------------------------------
6 m = 600 cm

------------------------------------------------------
Find the number of strips for 1 6m-board
------------------------------------------------------
Find the number of strips that can be cut from the 6m board.

600 ÷ 29 = 20 pieces remainder 20cm

So we can only cut 20 pieces of 29 strips from one 6m board.

------------------------------------------------------
Find number of boards needed
------------------------------------------------------
70 ÷ 20 = 3.5

We need 3.5 of the 6m boards.

Since she can't have half a board, she has to buy 4 pieces of the board.

------------------------------------------------------
Answer: 4 pieces of the 6m board.
------------------------------------------------------

7 0

3 years ago

Need help, Due ASAP!

VMariaS [17]

Stop posting on here and do the work yourself I usually don't mind helping people but in some cases, I need to just say do it by yourself look at notes look up the answer there are a million things you can do instead of spam posting all your questions good day

4 0

2 years ago

Read 2 more answers

While working at the drugstore, Grace earns $9.83 per hours. How many hours will it take grace to earn $49.15?

RoseWind [281]

Answer:

5

Step-by-step explanation:

all you have to do is divide 49.15 by 9.83.

7 0

2 years ago

Please help me asap in this!!!! ​

Please help me asap in this!!!!