Chapter 12.8, Problem 1P

To determine

To calculate: The volume of a pyramid varies jointly as the height and the area of the base where height is $8cm$ and area of the base is $39c{m}^2$ .

The height of a pyramid is $20cm$ , has a base area of $63c{m}^2$ and a volume of $420c{m}^3$ .

Answer to Problem 1P

The volume is $104c{m}^3$ .

Explanation of Solution

Given information:

The volume of a pyramid varies jointly as the height and the area of the base where height is $8cm$ and area of the base is $39c{m}^2$ .

The height of a pyramid is $20cm$ , has a base area of $63c{m}^2$ and a volume of $420c{m}^3$

Formula used:

For the volume of a pyramid:

  $v_1=h_1{A}_1$

For varies jointly:

  $\frac{v_1}{h_1{A}_1}=\frac{v_2}{h_2{A}_2}$

Calculation:

Consider, that the volume of a pyramid varies jointly as the height and the area of the base where height is $8cm$ and area of the base is $39c{m}^2$ .

The height of a pyramid is $20cm$ , has a base area of $63c{m}^2$ and a volume of $420c{m}^3$

Recall that For the volume of a pyramid:

  $v_1=h_1{A}_1$

For varies jointly:

  $\frac{v_1}{h_1{A}_1}=\frac{v_2}{h_2{A}_2}$

Therefore, volume of pyramid is given by,

  $\begin{array}{c}\frac{420}{20\times 63}=\frac{v_2}{39\times 8}\\ \frac{420\times 39}{20\times 63}=v_2\\ 104=v_2\end{array}$

Thus, the volume of the pyramid is: $104c{m}^2$ .