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A frustum of a pyramid is 16 cm Square at the bottom, 6Cm Square at the top and 12cm high. Find the volume of the frustum. ​

Respuesta :

[tex]\large\bf{\underline{Given:}}[/tex]

  • [tex]\bf{B_{1}=16 cm}[/tex]
  • [tex]\bf{B_{2}=6 cm}[/tex]
  • [tex]\bf{H = 12cm}[/tex]

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[tex]\large\bf{\underline{Using\: formula:}}[/tex]

[tex]\boxed{\bf\underline\pink{⟹\frac{h}{3} \times (b_1 + b_{2} + \sqrt{b_{1} } \times b_{2})}}[/tex]

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[tex]\large\bf{\underline{Therefore}}[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎[tex] \bf \: ⟹v = \frac{12}{3} \times (16 + 6 + \sqrt{16 \times 6)} [/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎[tex] \bf \: ⟹v = 4 \times (16 + 6 + 9.7979)[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎[tex] \bf \: ⟹v = 4 \times 31.7979[/tex]

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎[tex] \bf \: ⟹v = 127.1917[/tex]

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[tex]\large\bf{\underline{Hence}}[/tex]

[tex]\large\bf{⟹Volume=127.19{cm}^{2}(approx)}[/tex]

Answer: Consider the whole pyramid, before the top (with height h) was cut off to make the frustrum. Using similar triangles, the missing height is 36/5. So, the volume of the frustrum is

1/3 * 16^2 * (12 + 36/5) - 1/3 * 6^2 * 36/5 = 1552 cm^3   hope this helps - omarresendiz :)

Step-by-step explanation: