Question

13. a) A cuboid is twice as long as its breadth and its height is 4 cm. If the volume of the cuboid is 288 cm³,

(i) find its length and breadth.
(ii) Find its surface area.​

Answer 1

Let the breadth of the cuboid be x

and length be 2x

and height is given 4 cm

So,

`\boxed{ \purple{\mathfrak{ Volume = l * b * h}}}`

i) Length and breadth:

`\blue{\sf Volume = 2x * x * 4}`

`\blue{\sf 288 = 2x * x * 4}`

`\blue{\sf 288 = {8x}^(2) }`

`\blue{\sf 36 = {x}^(2) }`

`\blue{\sf √(36) = {x} }`

`\blue{\sf x = 6}`

Now,

`\boxed{ \green{\mathfrak{Length = 2x \implies 2×6 \implies 12\:cm}}} \\ \boxed{ \green{\mathfrak{Breadth = x \implies 6 cm}}}`

ii) Its surface area

We now have all the dimensions i.e.

• Length = 12 cm
• Breadth = 6 cm
• Height = 4 cm

`\pink { \tt \: Surface \: area = \: 2(lb + bh + hl) }`

`\orange { \sf \:S.A. = 2(12 * 6 + 6 * 4 + 12 * 4) }`

`\orange { \sf \:S.A. = 2(72+ 24 + 48) }`

`\orange { \sf \:S.A. = 2(144) }`

`\red { \sf \:S.A. = 288 {cm}^(2) }`

`\large{ \pink{ \mathfrak{ \underline{ \underline{ \overline{ \overline{ \purple{Hope \: it \: helps \: you}}}}}}}}`