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

Answers

volume = a^2(h/3)
a= 48 cm
h= 26 cm
Volume = 48^2 (26/3)
V=19968 cubic cm.
Hope that helped you
The volume of a square pyramid with base edges of 48 cm and a slant height of 26 cm = 7,680cm^3
The volume of a square pyramid can be derived from the expression that the volume of an object is equal to the product of the area of the base times its height. For a square pyramid, it can be simplified as V = a^2(h)/3 where a is the side of the square base and h is the height. However, we are given the slant height. The equation would be:

V = a^2(h)/3

s^2 = (a/2)^2 + h^2     where s is the slant height
h = √( s^2 - (a/2)^2)
h = √( 26^2 - (48/2)^2)= 10

V = 48^2(10)/3 = 7680 cm^3 --> OPTION C
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

The correct answer is 7,680 cm3 :D

Option C is the correct answer.

Step-by-step explanation:

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

We have

               s^2=h^2+\left ( \frac{b}{2}\right )^2

Here s = 26 cm and b = 48 cm

Substituting

      26^2=h^2+\left ( \frac{48}{2}\right )^2\\\\h^2=100\\\\h=10cm

\texttt{Volume of square pyramid, }V=\frac{1}{3}b^2h

Substituting

          V=\frac{1}{3}\times 48^2\times 10=7680cm^3

Option C is the correct answer.

                   

\text{V}=7,680\ cm^3

Step-by-step explanation:

The volume of a pyramid is given by :-

\text{Volume}=\dfrac{1}{3}\text{base area *height}

Given: Slant height of the pyramid (l)= 26 cm

The base edge of the pyramid (s)=48 cm

Now, the height of the pyramid is given by :

h=\sqrt{l^2-(\dfrac{s}{2})^2}\\\\\Rightarrow\ h=\sqrt{26^2-(\dfrac{48}{2})^2}\\\\\Rightarrow\ h=10\ cm

Now, the volume of the square pyramid is given by :-

\text{V}=\dfrac{1}{3}(48)^2(10)\\\\\Rightarrow\ \text{V}=7680\ cm^3

- C) 7,680\ cm^3


Explanation:-

Given: Base edge of square pyramid a= 48 cm

Slant height square pyramid l =26 cm

Let h be the height of the right pyramid

Thus,

h^2=l^2-(\frac{a}{2})^2=26^2-(\frac{48}{2})^2=676-576=100\\\\\Rightarrow\ h=\sqrt{100}=10

The volume of square pyramid=\frac{1}{3}a^2h=\frac{1}{3}(48)^2(10)=7680\ cm^3

Thus C is the right option.The volume of square pyramid= 7,680\ cm^3

The height of this pyramid will be:

√(26^2 - (48/2)^2) = 10cm

So the volume is: V = 1/3 * 48^2 * 10 = 7680 cm^3


Do you know the answer?

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