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Sagot :

fieryanswererft

Answer:

153 cubic feet

Step-by-step explanation:

V = kha .........where h is height and a area and V is volume

92 = k * 12 * 23

k = 92/(12*23) =1/3

if k, constant is 1/3

volume =1/3 * 17 * 27

=153 cubic feet

View image fieryanswererft
AadhPrit

Answer:

The volume of pyramid is 153 cubic feet with a height of 17 feet and a base with an area of 27 square feet.

Step-by-step explanation:

Given :

  • [tex]\small\green\bull[/tex] Height of pyramid = 12 feet
  • [tex]\small\green\bull[/tex] Base area of pyramid = 23 feet
  • [tex]\small\green\bull[/tex] Volume of pyramid = 92 cubic feet

[tex]\begin{gathered}\end{gathered}[/tex]

To Find :

  • [tex]\small\green\bull[/tex] The volume of a pyramid with a height of 17 feet and a base with an area of 27 square feet.

[tex]\begin{gathered}\end{gathered}[/tex]

Solution :

Mathematically, the relationship between the three variables is given by the expression :

[tex]\longrightarrow{\sf{V \: \alpha \: kHA}}[/tex]

[tex]\longrightarrow{\sf{V = kHA}}[/tex]

  • [tex]\pink\star[/tex] V = Volume
  • [tex]\pink\star[/tex] H = height
  • [tex]\pink\star[/tex] A = base area
  • [tex]\pink\star[/tex] k = constant

[tex]\rule{200}2[/tex]

Substituting all the given values in the formula to find k (constant) :

[tex]\begin{gathered} \qquad\longrightarrow{\sf{V = kHA}} \\ \\ \qquad\longrightarrow{\sf{92 = k \times 12 \times 23}} \\ \\ \qquad\longrightarrow{\sf{92 = k \times 276}} \\ \\ \qquad\longrightarrow{\sf{92 = 276k}} \\ \\ \qquad\longrightarrow{\sf{k = \dfrac{92}{276}}} \\ \\ \qquad\longrightarrow{\sf{k = \dfrac{\cancel{92}}{\cancel{276}}}} \\ \\ \qquad\longrightarrow{\sf{k = \frac{1}{3} \: feet}}\end{gathered}[/tex]

Hence, the value of k (constant) is 1/3 feet.

[tex]\rule{200}2[/tex]

Now, finding the volume of pyramid with height of 17 feet and a base with an area of 27 square feet by substituting the values in the formula :

[tex]\begin{gathered} \qquad\longrightarrow{\sf{V = kHA}} \\ \\ \qquad\longrightarrow{\sf{V = \dfrac{1}{3} \times 17 \times 27 }} \\ \\ \qquad\longrightarrow{\sf{V = \dfrac{1}{\cancel{3}} \times 17 \times \cancel{27 }}} \\ \\ \qquad\longrightarrow{\sf{V = 1\times 17 \times 9}} \\ \\ \qquad\longrightarrow{\sf{V = 17 \times 9}} \\ \\ \qquad\longrightarrow{\sf{V = 153 \: {feet}^{3} }}\end{gathered}[/tex]

Hence, the volume of pyramid ks 153 cubic feet.

[tex]\rule{300}{2.5}[/tex]

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