Question

three cubes whose edges measure 3cm,4cm,and 5cm respectively to form a single cube find its edge. Also find the surface area of new cube.​

Answer 1

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

$\Large{\mathcal{\underline{\underline{Given \ :-}}}}$

${\odot{}}$Edges of cubes = 3cm , 4cm and 5cm

$\Large{\mathcal{\underline{\underline{To \ find \ :-}}}}$

${\odot{}}$ Edge of new cube

${\odot{}}$ Surface area of new cube

$\Large{\mathcal{\underline{\underline{Solution \ :-}}}}$

${\purple{\star{}}}$ Since the small cubes are used to form the big cube.

${\therefore{}}$ Volume of big cube = Sum of volume of small cubes

${\boxed{\sf \ Volume \ of \ cube \ = \ {side}^{3} }}$

${\sf{\mapsto \ Volume \ of \ big \ cube \ = \ {3}^{3} + {4}^{3} + {5}^{3} }}$

${\sf{\mapsto \ Volume \ of \ big \ cube \ = \ 27+64+125 }}$

${\sf{\mapsto \ Volume \ of \ big \ cube \ = \ 216 {cm}^{3} }}$

${\mathfrack{\Large{Now}}}$

${\sf{\leadsto \ Volume \ of \ big \ cube \ = \ 216 {cm}^{3} }}$

${\sf{\leadsto \ {side}^{3} \ = \ 216 {cm}^{3} }}$

${\sf{\leadsto \ side \ = \ \sqrt[3]{216} }}$

${\sf{\leadsto \ side \ = \ 6 cm}}$

${\bold{\underline{\sf \ Hence \ edge \ of \ cube = 6 cm}}}$

${\boxed{\sf \ Surface \ area \ of \ cube = 6 {side}^{2} }}$

${\sf{\hookrightarrow \ Surface \ area \ of \ new \ cube = 6 \times 6 \times 6}}$

${\bold{\hookrightarrow \sf \ Surface \ area \ of \ new \ cube = 216 {cm}^{2} }}$