Question

The lengths of three unequal edges of rectangular solid block are in GP. The volume of the block is 216 $c{m}^3$ and the total surface area is 252 $c{m}^2$. The length of longest edge is

• A. 12 cm
• B. 6 cm
• C. 18 cm
• D. 3 cm

Answer 1

Answer: (A)

12 cm

Let the three unequal lengths of the block be $\frac{A}{r},AandAr$
the volume $A^3$ equals 216
$\Rightarrow A^3=216\Rightarrow A=6$
Also the total surface area =$2(\frac{A^2}{r}+A^2+A^{2}r)$
Hence $2(\frac{A^2}{r}+A^2+A^{2}r)=252\Rightarrow \frac{1}{r}+1+r=\frac{252}{2A^2}=\frac{252}{72}=\frac{7}{2}\Rightarrow \frac{1}{r}+r=\frac{5}{2}\Rightarrow \frac{1}{r}+r=\frac{1}{2}+2Hencer=2or\frac{1}{2}$
So the longest side= $6\times 2=12cm$