Respuesta :

KitdaAneek

Answer: Volume = 262 m³ 

Step-by-step explanation:

Hi again! We will need to use the volume of the cone formula and the given information to solve this problem. Make sure to convert diameter into radius before solving.

Volume of Cone equation : [tex]\begin{document}\begin{equation*}\fbox{\fbox{$V = \frac{1}{3} \pi r^2 h$}}\end{equation*}\end{document}[/tex]

Where:

  • r represents the radius of the cone(half of the diameter)
  • h represents the height of the cone

Using this information, we must half the diameter in order to get the radius:

[tex]d = 2r[/tex] → [tex]10=2r[/tex] → [tex]\fbox {r=5}[/tex]

Solving:

Given : [tex]r=5, h=10[/tex]

[tex]V = \frac{1}{3} \pi (5)^2 (10) \\[10pt] V = \frac{1}{3} \times \pi \times 25 \times 10 \\[10pt] V = \frac{250}{3} \pi \\[10pt] V \approx \frac{250}{3} \times 3.14 \\[10pt] V \approx 261.82 \, \text{cubic meters} \\[10pt] V \approx 262 \, \text{cubic meters}[/tex]

Rounded to the nearest whole number as stated in the problem.

That's it!

msm555

Answer:

Volume = 262 m³

Step-by-step explanation:

To find the volume of a cone, we can use the formula:

[tex] \textsf{Volume} = \dfrac{1}{3} \pi r^2 h [/tex]

where:

  • [tex] r [/tex] is the radius of the base,
  • [tex] h [/tex] is the height.

Given that the diameter ([tex] d [/tex]) is 10 m, the radius ([tex] r [/tex]) is half of the diameter.

So [tex] r = \dfrac{d}{2} = \dfrac{10}{2} = 5 [/tex] meters.

Now, substitute the values into the formula:

[tex] \textsf{Volume} = \dfrac{1}{3} \pi (5^2) \times 10 [/tex]

[tex] \textsf{Volume} = \dfrac{1}{3} \pi \times 25 \times 10 [/tex]

[tex] \textsf{Volume} = \dfrac{250}{3} \pi [/tex]

[tex] \textsf{Volume} = 83.33333 \dots  \times 3.141592654 [/tex]

[tex] \textsf{Volume} \approx 261.7993878 [/tex]

[tex] \textsf{Volume} = 262  \, \textsf{m}^3 \textsf{(in nearest whole number)}[/tex]

So, the volume of the cone is approximately [tex] 262 \, \textsf{m}^3 [/tex].

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