Question

SOMEONE PLEASE HELPP

What is the volume of the pyramid?


540 ft3

48 ft3

432 ft3

150 ft3

Answer 1

Answer: The volume of the pyramid is (B) 48 ft³.

Step-by-step explanation: We are given to find the volume of the pyramid shown in the figure.

The VOLUME of a pyramid with base area 'b' square units and height 'h' units is given by

`V=(1)/(3)bh.`

Here, the base is a square with side of length 6 ft, so the area of the base, 'b' is given by

`b=6* 6=36~\textup{square units}.`

Now, as shown in the modified attached figure, ABC is a right-angles triangle at ∠B, and AC is the slanting height of 5 ft.

AB is the height of the pyramid.

BC is equal to half of the side length of the square base, so we have

`BC=(6)/(2)=3~\textup{ft}.`

Now, using Pythagoras Theorem, we have

`AC^2=AB^2+BC^2\\\\\Rightarrow AB^2=AC^2-BC^2\\\\\Rightarrow AB=√(5^2-3^2)\\\\\Rightarrow AB=√(16)\\\\\Rightarrow AB=4~\textup{ft}.`

Hence, height of the pyramid, h = 4 ft.

Therefore, the volume of the Pyramid will be

`V=(1)/(2)* bh=(1)/(3)* 36* 4=48~\textup{ft}^3.`

Thus, the volume of the pyramid is 48 ft³.

Option (B) is correct.