(i) If the Lateral Surface Area of a cube is $900 c m^{2}$ , find the length of its side.
(ii) If the Total Surface Area of a cube is $1014 c m^{2}$ , find the length of its side.
(iii) The volume of the cube is $125 d m^{3}$ . Find its side

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Solution

i) LSA of cube $= 900 c m^{2} \Rightarrow 4 a^{2} = 90 \Rightarrow a = \sqrt{225} = 15 c m$
ii)TSA of cube $= 1014 c m^{2} \Rightarrow 6 a^{2} = 1014 \Rightarrow a = \sqrt{169} = 13 c m$
iii)Volume of cube $= 125 d m^{3} \Rightarrow a^{3} = 125 \Rightarrow a = \sqrt[3]{125} = 5 c m$

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