Respuesta :

volume of the composite figure = volume of cylinder - volume of cone

volume of cylinder = πr²h

[tex] \frac{22}{7} \times 8 \times 8 \times 12 \\ \\ = > \frac{16896}{7} \: ft {}^{3} [/tex]

volume of cone = 1/3 πr²h

[tex] \frac{1}{3} \times \frac{22}{7} \times 8 \times 8 \times 12 \\ \\ = > \frac{16896}{21} \: ft {}^{3} [/tex]

[tex]total \: volume = \frac{16896}{7} - \frac{16896}{21} \\ \\ = > \frac{50688 - 16896}{21} \\ \\ = > \frac{33792}{21} \\ \\ = > 1609.14 \: ft {}^{3} (approx.)[/tex]

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Answer:

[tex]\large\boxed{\sf\: Volume \: of \: the \: figure\: \approx \: 1607.68\: feet^{3}}[/tex]

Step-by-step explanation:

We need to find the volume of each composite figure given in the question. Here, the figures are ⟶ a cylinder & a cone.

Given,

  • Radius (r) = 8 feet
  • Height (h) = 12 feet
  • Take the value of π = 3.14

NOTE: The values of the radius & the height of both the figures remain the same as the cone is fit inside the cylinder.

The formulae of the volume of the figures are [tex]\downarrow[/tex]

  • Cylinder = πr²h
  • Cone = ⅓ πr²h

So,

Volume of cylinder

= πr²h

= 3.14 × (8)² × 12

= 2,411.52 feet³ (approx.)

Volume of cone

= ⅓ πr²h

= ⅓ × Volume of cylinder

= ⅓ × 2,411.52

= 803.84 feet³ (approx.)

Thus, the total volume of the figure

= Volume of cylinder - Volume of the cone

= 2,411.52 - 803.84

= 1,607.68 feet³ (approx.)

•°• Total volume of the composite figure = 1,607.68 feet³ (approx)

_______________

Hope this helps!

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