The lateral surface area of a cube is $324 \mathrm{~cm}^{2}$. Find its volume and the total surface area.
in Mathematics
26 views
2 Votes
2 Votes
The lateral surface area of a cube is $324 \mathrm{~cm}^{2}$. Find its volume and the total surface area.
in Mathematics
by
7.2k Points

1 Answer

1 Vote
1 Vote
 
Best Answer

Solution

Let each side of the cube be $a \mathrm{~cm}$.

Then, the lateral surface area of the cube $=\left(4 a^{2}\right) \mathrm{cm}^{2}$.

$\therefore \quad 4 a^{2}=324 \Rightarrow a^{2}=81 \Rightarrow a=\sqrt{81}=9$.

Volume of the cube $=a^{3} \mathrm{~cm}^{3}$

=(9 × 9 × 9) cm³ =729 cm³ 

Total surface area of the cube $=\left(6 a^{2}\right)$ sq units

= (6 ×9 ×9) cm³ = 486 cm³

by
7.2k Points

Related Questions

Welcome To Informesia

Informesia Helps You To Prepare India's All States Board Exams (CBSE, ICSE, UP Board, BSEB, HPBOSE, RBSE, MSBSHSE) and Competitive Exam Like JEE (Main + Advanced), AIIMS, NEET, KVPY, NTSE, BITSAT, Olympiad, CLAT...etc.
For Any Query or Suggestion, Please Contact us on :
[email protected]

Connect us on Social Media