Question

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Answer 1

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 :

• $\small\green\bull$ 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) :

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

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 :

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

Hence, the volume of pyramid ks 153 cubic feet.

$\rule{300}{2.5}$

Answer 2

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