Question

Mr. Balbin will build a rectangular pyramid whose volume is 28 cubic meters. If the length of the base is 1 meter more than the width and its height is 4 meters more than the width, find the measurement of the length, width, and height of the rectangular pyramid.

NOTE: show your solution

Answer 1

Step-by-step explanation:

length = 4m

width = 3m

height = 7m

Step-by-step explanation:

formula for the volume of a rectangular pyramid is \frac{lwh}{3}

3

lwh

the problem said that the volume is 28 so \frac{lwh}{3}=28

3

lwh

=28

the conditions for the length can be written as width + 1 and the height is width + 4 or in equation form:

l = w + 1l=w+1

h = w + 4h=w+4

going back to \begin{gathered}\frac{lwh}{3}=28\\\end{gathered}

3

lwh

=28

, just replace the letter with the equation so:

instead of l it would be w + 1 and instead of h it would be w + 4, it would look like this:

\frac{(w+1)(w)(w+4)}{3}=28

3

(w+1)(w)(w+4)

=28 , then just find w, which is: w = 3w=3

then go back to the equation of the length and height and replace the w with 3 so it would be:

l=3+1\\h=3+4\

l=3+1

h=3+4

so length = 4, width = 3, height = 7

Answer 2

Given:

Mr.Balbin will build a rectangular pyramid whose volume is 28 cubic meters.

The length of the base is 1 meter more than the width.

The height is 4 meters more than the width.

To find:

The measurement of the length, width, and height of the rectangular pyramid.

Formula to be used:

Volume of rectangular pyramid = $\frac{1}{3}$ × length × height × width

Solution:

Let the width of the rectangular pyramid be 'w'

The length of the base is 1 meter more than the width.

Length, l = w + 1

The height is 4 meters more than the width.

Height, h = w + 4

Volume of the rectangular pyramid = 28 cubic meters

Volume of rectangular pyramid = $\frac{1}{3}$ × length × width × height

28 =  $\frac{1}{3}$ × (w + 1) × (w + 4) × w

28 × 3 = (w + 1) × (w + 4) × w

4 × 7 × 3 = (w + 1) × (w + 4) × w

By comparing L.H.S and R.H.S

(3 + 1) × (3 + 4) × 3 = (w + 1) × (w + 4) × w

Therefore,

w = 3 m

Length, l = 3 + 1

l = 4 m

Height, h = 3 + 4

h = 7 m

Final answer:

The measurement of the length, width, and height of the rectangular pyramid are 4 m, 3 m and 7 m respectively.