Question

The volume of a cone is 183.26 cubic feet and its radius is 5 feet. What is the cone's height? Round to the nearest foot. Use 3.14 for \pi .

Answer 1

@DaBest21

Answer 2

here we have to use this formula:
\[\Large V = \frac{{\pi {r^2}h}}{3}\]

Answer 3

where V is the volume of the cone, r is the radius of its base, and h is the height of the cone

Answer 4

\[3\frac{ 183.26}{ 3.14*5*5 }\]is the formula @Aliypop

Answer 5

so do 3.14*5*5 first @Aliypop

Answer 6

from that formula above we get:
\[h = \frac{{3V}}{{\pi {r^2}}} = \frac{{3 \times 183.26}}{{3.14 \times 5 \times 5}} = ...feet\]

Answer 7

78.5

Answer 8

yep now do 183.26/78.5

Answer 9

2.33452293

Answer 10

hint:
\[h = \frac{{3V}}{{\pi {r^2}}} = \frac{{3 \times 183.26}}{{3.14 \times 5 \times 5}} = 3 \times 2.335 = ...feet\]

Answer 11

2.3335

Answer 12

what's the next step ?

Answer 13

as I wrote before, what is:
3*2.335=...?

Answer 14

7.005

Answer 15

that's right!

Answer 16

so7.005 is the answer?

Answer 17

yes!

Answer 18

no

Answer 19

u have to round

Answer 20

okay :D

Answer 21

@Aliypop round

Answer 22

yes! sorry @Aliypop you have to round off to the hearest unit of foot

Answer 23

nearest*

Answer 24

so what does 0 tell u to do to 7 Hint less than 5 means stay the same

Answer 25

so would it be 8.00

Answer 26

no it would be 7 Don't forget to medal and fan if you already haven't. Plus send me a message if you need more help @Aliypop

Answer 27

Carson's Bakery and Chocolate Shop is experimenting with making chocolate in the shape of different types of sports equipment. Bayside High School's Volleyball team has ordered 100 solid white chocolate volleyballs. What volume of white chocolate is needed to fill this order if the radius of each volleyball is 4 cm? Rounded to the nearest tenth of a cubic centimeter. Use 3.14 for \pi .

Answer 28

it appeared wrong again

Answer 29

we did this already didnt we? @Aliypop

Answer 30

@welshfella

Answer 31

@welshfella @welshfella

Answer 32

I got 211 now as the answer

Answer 33

hint:
the volume V of a sphere is given by the subsequent equation (pi=3.14):
\[\begin{gathered}
V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {r^3} = \hfill \\
\hfill \\
= \frac{{12.56}}{3} \times {4^3} = \frac{{12.56}}{3} \times 64 = ...? \hfill \\
\end{gathered} \]

Answer 34

2,411.25

Answer 35

I got this:
\[\begin{gathered}
V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {r^3} = \hfill \\
\hfill \\
= \frac{{12.56}}{3} \times {4^3} = \frac{{12.56}}{3} \times 64 = 267.85c{m^3} \hfill \\
\end{gathered} \]

Answer 36

okay

Answer 37

so 267.9

Answer 38

sorry I have made an error, here is the right result:
\[\begin{gathered}
V = \frac{{4 \times 3.14}}{3}{r^3} = \frac{{12.56}}{3} \times {r^3} = \hfill \\
\hfill \\
= \frac{{12.56}}{3} \times {4^3} = \frac{{12.56}}{3} \times 64 = 267.9466c{m^3} \hfill \\
\end{gathered} \]

so the total volume of the requested chocolate is:
\[V = 100 \times 267.9466 = 26794.66 \cong 26794.7c{m^3}\]

Answer 39

okay

Answer 40

so rounded to the nearest foot it is 267.9

Answer 41

267.9 is the volume of a single volleyball

Answer 42

the requested volume of needed white chocolate is:
\[V \cong 26794.7c{m^3}\]

Answer 43

The new business building uptown is building a wall made entirely of glass pyramids. Each pyramid will have a square base with length of 8 inches and height of 10 inches. If the wall requires 250 of these pyramids, what volume of glass will be used? Round to the nearest cubic inch.

Answer 44

we have to compute the volume V of a single pyramid. So, we can apply this formula:
\[\Large V = \frac{1}{3}L \times L \times H\]
where L is the length of the square base, and H is the height of the pyramid:

Answer 45

okay

Answer 46

substituting your data, we have:
\[\begin{gathered}
V = \frac{1}{3}L \times L \times H = \hfill \\
\hfill \\
= \frac{1}{3}8 \times 8 \times 10 = \frac{{640}}{3} = ...inche{s^3} \hfill \\
\end{gathered} \]

Answer 47

213.333333

Answer 48

correct!

Answer 49

Now, we have 250 of such pyramids, so the requested volume of needed glass, is:
\[{V_{TOTAL}} = 213.3333 \times 250 = \]

Answer 50

53,33.333333

Answer 51

that's right! Now we have to round off that result to the nearest unit, so we get:
\[{V_{TOTAL}} = 213.3333 \times 250 = {\text{53333}}{\text{.325}} \cong {\text{53333}}inche{s^3}\]

Answer 52

ok