Question

The surface area of $3$ different surfaces of a cuboid is $150{cm}^2$, $75{cm}^2$ & $50{cm}^2$. Find volume of cuboid.

Answer 1

Total surface area of a cuboid of length ${}^{\prime }{l}^{\prime }$ , breadth ${}^{\prime }{b}^{\prime }$ and height ${}^{\prime }{h}^{\prime }$ is

$TSA=2(lb+bh+lh)$

Given:-

$l\times b=150{cm}^{2}b\times h=75{cm}^{2}h\times l=50{cm}^2$

We know that volume of cuboid is

$V=l\times b\times h$

Squaring both the sides

$V^2=l^2\times b^2\times h^2\Rightarrow V^2=l\times l\times b\times b\times h\times h\Rightarrow V^2=(l\times b)(b\times h)(l\times h)\Rightarrow V=\sqrt{(l\times b)(b\times h)(l\times h)}$

From the given equations

$\Rightarrow V=\sqrt{150\times 75\times 50}\Rightarrow V=\sqrt{5^2\times 3\times 2\times 5^2\times 3\times 5^2\times 2}\Rightarrow V=\sqrt{5^6\times 3^2\times 2^2}\Rightarrow V=5^3\times 3\times 2\Rightarrow V=125\times 6\Rightarrow V=750{cm}^3$