Question

Find the volume of the pyramid. Round to the nearest tenth if necessary.

Question 3 options:

15,120 ft3

5,040 ft3

15,498 ft3

5,166 ft3

Answer 1

You need to remember Formula for Volume of rectangular pyramid

Volume = LBH/3

L,B,H represents usual notation length ,breadth,height respectively

Here 41ft is hypotenuse

So first we need Height

As apex lies above Centre

Hence Base = 18/2 = 9

Now Height = √(41^2 -9^2)

= √1681-81

= √1600

= 40

Now We can easily find Volume

L= 21

B= 18

H= 40

Volume = 21×18×40/3

= 7× 18 × 40

= 5040 ft3

Answer 2

For this case we have that by definition, the volume of a pyramid is given by:

`V = \frac {A_ {b} * h} {3}`

Where:

`A_ {b}:` It is the area of the base

h: It is the height

We have that the base is square, so the area is:

`A_ {b} = 18 * 21 = 378 \ ft ^ 2`

On the other hand, we can find the height by the Pythagorean theorem:

`h = \sqrt {41 ^ 2 - (\frac {18} {2}) ^ 2}\\h = \sqrt {41 ^ 2- (9) ^ 2}\\h = \sqrt {1681-81}\\h = \sqrt {1600}\\h = 40 \ ft`

Finally, the volume is:

`V = \frac {378 * 40} {3}\\V = 5040 \ ft ^ 3`

Answer:

Option B