Question

Find the volume of a square pyramid with base edges of 48 cm and a slant

height of 26 cm.
A.
11,520 cm3

B.
23,040 cm3

C.
7,680 cm3

D.
768 cm3

Answer 1

Firstly, write the stuffs you already know.

Length = Width = 48, Slant Height = 26.
You need to find Height of the pyramid.

Using Pythagoras Theory:
h = ✓26^2 - (48/2)^2
h = 10

Now apply the pyramid volume formula;
Volume = (Length×Width×Height)/3
Thus, v = (48^2 × 10)/3
v = 7680 cm^3

Answer 2

Option C is the correct answer.

Explanation:

Let the base edge be b, slant height be s and perpendicular height be h.

We have

`s^2=h^2+\left ( (b)/(2)\right )^2`

Here s = 26 cm and b = 48 cm

Substituting

`26^2=h^2+\left ( (48)/(2)\right )^2\\\\h^2=100\\\\h=10cm`

`\texttt{Volume of square pyramid, }V=(1)/(3)b^2h`

Substituting

`V=(1)/(3)* 48^2* 10=7680cm^3`

Option C is the correct answer.