Question

Dimensions of a closed wooden box are in the ratio 5: 4:3. If cost of painting its outer surface
excluding the base at the rate of 5 per sq dm is 9250, find the dimensions of the box.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Dimensions of a closed wooden box are in the ratio 5: 4:3.

Let assume that

Length of the wooden box, l = 5x dm

Breadth of the wooden box, b = 4x dm

Height of the wooden box, h = 3x dm

So,

Outer Surface Area of wooden box excluding the base is equals to Curved Surface Area of wooden box + Area of top of the box.

Thus,

$\rm\implies \:Surface Area_{box}$

$\rm \:  =  \: 2(l + b)h + lb$

$\rm \:  =  \: 2(5x + 4x)(3x) + (5x)(4x)$

$\rm \:  =  \: 6x(9x) + {20x}^{2}$

$\rm \:  =  \: {54x}^{2} + {20x}^{2}$

$\rm \:  =  \: {74x}^{2}$

$\rm\implies \:\boxed{\tt{ Surface Area_{box} = {74x}^{2} }} - - - - (1)$

Now, Further given that

The Cost of painting its outer surface excluding the base at the rate of Rs 5 per sq dm is Rs 9250.

So, it means

$\rm\implies \:Surface Area_{box} = \dfrac{9250}{5}$

$\rm\implies \:\boxed{\tt{ Surface Area_{box} = 1850 \: {dm}^{2} }} - - - - (2)$

So, on equating equation (1) and (2), we get

$\rm :\longmapsto\: {74x}^{2} = 1850$

$\rm :\longmapsto\: {x}^{2} = 25$

$\bf\implies \:x = 5$

Hence,

Length of the wooden box, l = 5 × 5 = 25 dm

Breadth of the wooden box, b = 4 × 5 = 20 dm

Height of the wooden box, h = 3 × 5 = 15 dm

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LEARN MORE

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T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

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T.S.A of cuboid = 2(lb + bh + lh)

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