Question

A frustum of a pyramid has an upper base $100m$ by $10m$ and a lower base of $80m$ by $8m$. if the altitude of the frustum is $5m$, find its volume (in cu. m).

• A. $4567.67$
• B. $3873.33$
• C. $4066.67$
• D. $2345.98$

Answer 1

The correct option is C $4066.67$

Give : Height of pyramid$\left(h\right)=5m$

It is a pyramid with rectangular base.

Edge of upper base $length\left(L\right)=100m,breadth\left(B\right)=10m$

Edge of lower base $length\left(l\right)=80m,breadth\left(b\right)=8m$

Area of upper base$\left(A_1\right)=L\times B=100\times 10=1000m^2$

Area of lower base$A_2=l\times b=640m^2$

Volume of frustum$\left(V\right)=\frac{h}{3}(A_1+A_2+\sqrt{A_1\times A_2})$

$⟹$$\left(V\right)=\frac{5}{3}(1000+640+\sqrt{1000\times 640})$

$=\frac{5}{3}(1640+800)=\frac{5}{3}\left(2440\right)=4066.666667$

Hence, volume$\left(V\right)=4066.67cu.m$