Question 109

External dimensions of a closed wooden box are in the ratio 5 : 4 : 3. If the cost of painting its outer surface at the rate of Rs. 5 per $d m^{2}$ is Rs. 11750, find the dimensions of the box.

Open in App

Solution

External dimensions of a closed wooden box are in the ratio 5 : 4 : 3
Let the external dimensions of the closed wooden box be 5x, 4x and 3x
The cost of painting = Rs. 5 per dm^2
Total cost of painting = Rs. 11750
$∴$ Total surface area $= \frac{T o t a l c o s t o f p a i n t i n g}{C o s t o f p a i n t i n g p e r d m^{2}} = \frac{11750}{5}$
$= 2350 d m^{2}$
Total surface area of a cuboid
$= 2 (l b + b h + h l) = 2 (5 x \times 4 x + 4 x \times 3 x + 3 x \times 5 x) = 2 (20 x^{2} + 12 x^{2} + 15 x^{2}) = 2 \times 47 x^{2} = 94 x^{2}$
Since, total surface area $= 2350 d m^{2}$
$\Rightarrow 94 x^{2} = 2350 \Rightarrow x^{2} = \frac{2350}{94} = 25 ∴ x = 5$
Hence, dimensions of the box are $5 x \times 5 = 25 d m, 4 x \times 5 = 20 d m$ and $3 x \times 5 = 15 d m$

Suggest Corrections

Similar questions

Question 109

External dimensions of a closed wooden box are in the ratio 5 : 4 : 3. If the cost of painting its outer surface at the rate of Rs. 5 per $d m^{2}$ is Rs. 11750, find the dimensions of the box.

Q. The dimensions of a rectangular box are in the ratio

4 : 2 : 3

. The difference between cost of covering it with paper at Rs.

12

per

m^{2}

and with paper at the rate of

13.50

per

m^{2}

is Rs.

1, 248

. Find the dimensions of the box.

Q. The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rates of Rs 8 and Rs 9.50 per m² is Rs. 1248. Find the dimensions of the box.

The dimensions of a reactangular box are in the ratio 2:3:4 and the difference between the cost of covering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per $m^{2}$ is Rs. 1,248. Find the dimensions of the box.

The outer dimensions of a closed wooden box are $10 c m$ by $8 c m$ by $7 c m$ Thickness of the wood is $2 c m$ . Find the total cost of wood to make box, if $1 c m^{3}$ of wood cost $R s .2 .00$ .

Join BYJU'S Learning Program

Question 109 External dimensions of a closed wooden box are in the ratio 5 : 4 : 3. If the cost of painting its outer surface at the rate of Rs. 5 per dm2 is Rs. 11750, find the dimensions of the box.

Question 109

External dimensions of a closed wooden box are in the ratio 5 : 4 : 3. If the cost of painting its outer surface at the rate of Rs. 5 per $d m^{2}$ is Rs. 11750, find the dimensions of the box.