Question

three cubes each of volume 125 cm³ are joining end-to-end to form a cuboid. Find the total surface area of cuboid ​

Answer 1

Given:

• Volume of cube = 125 cm³

To Find:

• Total surface area of cuboid.

Solution:

If volume of cube is 125 cm³

Then,

→ side³ = 125 cm³

→ side = ³√125

→ side = 5 cm

•°• If cubes are joined, then it will form a cuboid of length = 5 + 5 + 5 = 15

• Breadth = 5 cm
• Height = 5 cm

Total surface area of cuboid formed = 2(lb + bh + hl)

→ 2 [(15 × 5) + (5 × 5) + (15 × 5)]

→ 2 (75 + 25 + 75)

→ 2 × 175

→ 350 cm³

Hence,

• Total surface area of cuboid formed = 350 cm³.

Answer 2

$\large\underline\bold{ANSWER \red{\huge{\checkmark}}}$

$\pink{\overbrace{ \underbrace{ \red{\mid\star\mid \:\: \purple{ T.S.A\:of\:cuboid\:is\:350cm^2} } \:\: \red{\mid\star\mid}}}}$

EXPLANATION IN DETAILS

$\large\underline\bold{GIVEN,}$

$\leadsto volume\:of\:one\:cube \: is\: 125cm^3 \\ \\ \leadsto there \:are\:three\:such\:cubes\:coming \\ \\ together \:and\:forming\:a\:cuboid.$

$\large\underline\bold{TO\:FIND,}$

$\green{ \circ\: total\:surface\:area\:of\:forming\:cuboid\:by\:three\:cubes.}$

$\bf{ \mathcal{ \underline{\orange{Using\: Formula ,}}}} \\ \\ \rm{ \boxed{ \underline{ \red{total\:surface\:area\:of\:cuboid:- \blue{2[ lb+bh+hl] } } }}}$

$\natural \: first\:finding\:side\:of\:cube\:and\:rejoining\: dimension\:sides\: \\ \\ and \:finding\:length\:breadth\:and\:height\\ of\:formed\:cuboid \:and\:then\:finding\:the\:T.S.A.\:of\:cuboid.$

$\large\underline\bold{SOLUTION,}$

$\therefore Volume\:of\:cube \:is\:\pink{125cm^3 } \\ \star\:\:formula\:for\:Volume\:of\:cube\: is \: \\ \\ \underline{ \blue{ \bold{\mid\star\mid\:\:\:\:\: S^3\:\:\:\:\:\mid\star\mid}}} \:\: \\ \\ \mid\implies S^3= 125 \\ \\ \mid\implies S= \sqrt[3]{125} \\ \\ \mid\implies S= 5 \\ \\ \underline{\overline{ \mid \:\green{S=5cm } \: \mid}} \\ \\ \leadsto Height\:of \:cuboid\:is\: 5cm \\ \\ \leadsto breadth\:will\:also\:be\: 5cm \\ \\ \leadsto\: length\:of\:cuboid\:will\:be \: \times 3 \:because \\ \\ \:three\:cubes\:attaching\:together\:forms\:a\:cuboid. \:\: \\ \\ \leadsto \red{ 3\times 5 = 15cm }$

$\\ \\ \sf{ \boxed{ \blue{ \overline{\underline{ \mid\heartsuit\mid \: L=15cm , b= 5cm, h=5cm \: \mid\heartsuit \mid }}}}}$

$\\ \\ \clubsuit \: \: \blue{ Now\:finding\:the\:T.S.A \:of\:cuboid .\: }$

$\therefore by\:given\:formula \\ \\ \rightarrow \: \red{total\:surface\:area\:of\:cuboid \leadsto 2[lb+bh+hl]} \\ \\ \mid\implies 2\times \bigg[ (15\times 5)+(5\times 5)+(15\times 5)\bigg] \\ \\ \mid\implies 2\times \bigg[ 75+25+75\bigg] \\ \\ \mid\implies 2\times \bigg[ 150+25\bigg] \\ \\ \mid\implies 2\times \big[ 175\big] \\ \\ \mid\implies 350cm^2$

$\rm{ \boxed{ \blue{ \overline{\underline{ \red{\mid\heartsuit\mid \: \: \green{T.S.A\:of\:cuboid\:is\:350cm^2}\:\: \mid\heartsuit \mid }}}}}}$