Question

the total surface area of a cuboid is 495 CM square if the length and height of the cuboid are 15 cm and 6 cm find its breadth​

Answer 1

Given - Total surface area, length and height of a cuboid are 495cm², 15cm and 6cm respectively.

To Find - Breadth of the cuboid.

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Here

$\ \: \: \: \: \: \: \:$

• Length of the cuboid (l) = 15cm
• Height of the cuboid (h) = 6cm

$\ \: \: \: \:$

As we know that :

$\ \: \:$

$\underline{\boxed{\tt\purple{\bigstar \: T.S.A \: of \: a \:cuboid \: = 2(lb + bh + lh) }}}$

$\ \: \:$

Put the values :

$\ \: \:$

$\tt:\implies \: 495 = 2 [(15 \times b) + (b \times 6) + (15 \times 6)] \\ \\ \\ \tt:\implies \: 495 = 2[15b + 6b + 90] \\ \\ \\ \tt:\implies \: 495 = 2[21b + 90] \\ \\ \\ \tt:\implies \: 495 = 42b + 180 \\ \\ \\ \tt:\implies \: 495 - 180 = 42b \\ \\ \\ \tt:\implies \: 315 = 42b \\ \\ \\ \tt:\implies \: b = \cancel\frac{315}{42} \\ \\ \\ \tt:\implies \: b =\underline{\boxed{\sf\purple{7.5cm}}} \bigstar \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: breadth \: of \: the \: cuboid \: is \: \bold{7.5cm}.}}$

Answer 2

Answer:

Given :-

• TSA of cuboid = 495 cm²
• Length = 15 cm
• Height = 6 cm

To Find :-

Breadth

Solution :-

As we know that

$\pink \star {\green {\sf{TSA = 2(lb + bh + lh)}}}$

$\sf \: 495 = 2(15 \times b + b \times 6 + 15 \times 6)$

$\sf \: 495 = 2(15b + 6b + 90)$

$\sf \: 495 = 30b + 12b + 180$

$\sf \: 495 = 42b + 180$

$\sf \: 495 - 180 = 42b$

$\sf \: 315 = 42b$

$\sf \: b = 7.5 \: cm$

Hence :-

Breadth of cuboid is 7.5 cm