Respuesta :
Answer:
[tex]336\text{ cm}^3[/tex]
Step-by-step explanation:
GIVEN: A wooden model of a square pyramid has a base edge of [tex]12\text{ cm}[/tex] and an altitude of [tex]8\text{ cm}[/tex]. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and a frustum. Each base edge of the smaller pyramid is [tex]6\text{ cm}[/tex] and its altitude is [tex]4\text{ cm}[/tex].
TO FIND: Volume of frustum.
SOLUTION:
Base edge of bigger square pyramid [tex]=12\text{ cm}[/tex]
Altitude of bigger square pyramid [tex]=8\text{ cm}[/tex]
area of square base [tex]=\text{side}\times\text{side}=12\times12\text{ cm}^2[/tex]
[tex]=144\text{ cm}^2[/tex]
Volume of pyramid [tex]=\frac{1}{3}\times\text{base area}\times\text{height}[/tex]
putting values
[tex]=\frac{1}{3}\times144\times8[/tex]
[tex]=384\text{ cm}^3[/tex]
Base edge of smaller pyramid [tex]=6\text{ cm}[/tex]
Altitude of smaller pyramid [tex]=4\text{ cm}[/tex]
area of square base [tex]=6\times6=36\text{ cm}^2[/tex]
Volume of small pyramid [tex]=\frac{1}{3}\times36\times4[/tex]
[tex]=48\text{ cm}^3[/tex]
Volume of frustum [tex]=\text{Volume of bigger pyramid}-\text{volume of smaller pyramid}[/tex]
[tex]=384-48[/tex]
[tex]=336\text{ cm}^3[/tex]
Hence the volume of frustum is [tex]336\text{ cm}^3[/tex]
