Question

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Answer 1

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 :

• 
  `\small\green\bull` Height of pyramid = 12 feet
• 
  `\small\green\bull` Base area of pyramid = 23 feet
• 
  `\small\green\bull` Volume of pyramid = 92 cubic feet

`\begin{gathered}\end{gathered}`

To Find :

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

`\begin{gathered}\end{gathered}`

Solution :

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

`\longrightarrow{\sf{V \: \alpha \: kHA}}`

`\longrightarrow{\sf{V = kHA}}`

• 
  `\pink\star` V = Volume
• 
  `\pink\star` H = height
• 
  `\pink\star` A = base area
• 
  `\pink\star` k = constant

`\rule{200}2`

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

`\begin{gathered} \qquad\longrightarrow{\sf{V = kHA}} \\ \\ \qquad\longrightarrow{\sf{92 = k * 12 * 23}} \\ \\ \qquad\longrightarrow{\sf{92 = k * 276}} \\ \\ \qquad\longrightarrow{\sf{92 = 276k}} \\ \\ \qquad\longrightarrow{\sf{k = (92)/(276)}} \\ \\ \qquad\longrightarrow{\sf{k = \frac{\cancel{92}}{\cancel{276}}}} \\ \\ \qquad\longrightarrow{\sf{k = (1)/(3) \: feet}}\end{gathered}`

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

`\rule{200}2`

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 :

`\begin{gathered} \qquad\longrightarrow{\sf{V = kHA}} \\ \\ \qquad\longrightarrow{\sf{V = (1)/(3) * 17 * 27 }} \\ \\ \qquad\longrightarrow{\sf{V = \frac{1}{\cancel{3}} * 17 * \cancel{27 }}} \\ \\ \qquad\longrightarrow{\sf{V = 1* 17 * 9}} \\ \\ \qquad\longrightarrow{\sf{V = 17 * 9}} \\ \\ \qquad\longrightarrow{\sf{V = 153 \: {feet}^(3) }}\end{gathered}`

Hence, the volume of pyramid ks 153 cubic feet.

`\rule{300}{2.5}`

Answer 2

153 cubic feet

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