Question

. The dimensions of a cuboid are in the ratio 3:2:2 and the lateral surface area of the cuboid is 200 m2
. The outer surface of the cuboid is painted with eŶaŵel at the rate of ₹ 10 per m2. Find the total cost of painting the outer surface of the cuboid. ;₹ 3200)

Answer 1

Answer:

Total cost of painting the cuboid = Rs.3200

Step-by-step explanation:

Given:

• The dimensions of cuboid are in the ratio 3 : 2 : 2
• Cost of painting = Rs 10 per m²

To Find:

• Total cost of painting

Concept:

First find the dimensions of the cuboid. Next find the total surface area and multiply it with the cost per m² to find the total cost of painting the cuboid.

Solution:

First we have to find the dimensions of the cuboid.

Let the length of the cuboid be 3x.

Let the breadth of the cuboid be 2x.

Let the height of the cuboid be 2x.

Now by given,

Lateral surface area of the cuboid = 200 m²

But we know that,

LSA of a cuboid = 2h (l + b)

where h is the height

           l is the length

           b is the breadth

Hence,

2h (l + b) = 200

Substitute the data,

2 × 2x (3x + 2x) = 200

4x × 5x = 200

20x² = 200

x² = 200/20

x² = 10

x = √10

Hence,

Length of cuboid = 3x = 3√10 m

Breadth of cuboid = 2x = 2√10 m

Height of cuboid = 2x = 2√10 m

Now we have to find the total surface area of the cuboid.

TSA of a cuboid is given by,

TSA of cuboid = 2 (lb + bh + hl)

Substitute the data,

TSA of cuboid = 2 (3√10 × 2√10 + 2√10 × 2√10 + 2√10 × 3√10)

TSA of cuboid = 2 ( 60 + 40 + 60)

TSA of cuboid = 2 × 160

TSA of cuboid = 320 m²

Hence total surface area of cuboid is 320 m²

Now we have to find the total cost of painting.

Total cost of painting = TSA × Cost per m²

Substitute the data,

Total cost of painting = 320 × 10

Total cost of painting = 3200 rupees.

Hence the total cost of painting the cuboid is Rs.3200.

Answer 2

$\sf\large\underline{Let:-}$

$\sf{\implies The\: dimensions\:_{(cuboid)}=x}$

$\sf{\implies The\: length\:_{(cuboid)}=3x}$

$\sf{\implies The\: breadth\:_{(cuboid)}=2x}$

$\sf{\implies The\: height\:_{(cuboid)}=2x}$

$\sf\large\underline{Given:-}$

$\sf{\implies Lateral\:surface\:area=200m^2}$

$\sf{\implies Outer\: surface\:_{(painting\:rate)}=Rs.10\:per\:m^2}$

$\sf\large\underline{To\:Find:-}$

$\sf{\implies Total\:cost\:of\: painting_{(outer\: surface)}=?}$

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

To calculate the total cost of painting of outer surface area of cuboid , at first we have to calculate it's dimensions by helping of lateral surface area of cuboid. Then calculate the total cost of painting of outer surface area. By applying formula you can easily find out the total cost of painting:

$\sf\large\underline{Formula:-}$

$\sf{\implies L.S.A\:_{(cuboid)}=2(length+breadth)*height}$

• Substituting the value here:-]

$\tt{\implies 2(3x+2x)*2x=200}$

$\tt{\implies 2*5x*2x=200}$

$\tt{\implies 20x^2=200}$

$\tt{\implies x^2=10}$

$\tt{\implies x=\sqrt{10m}}$

• Now calculate outer surface area:-]

$\sf{\implies The\: length\:_{(cuboid)}=3x=3\sqrt{10}}$

$\sf{\implies The\: breadth\:_{(cuboid)}=2x=2\sqrt{10}}$

$\sf{\implies The\: height\:_{(cuboid)}=2x=2\sqrt{10}}$

$\sf{\implies Area\:_{(outer\: surface)}=2(lb+bh+lh}$

$\tt{\implies 2(3\sqrt{10}*2\sqrt{10}+2\sqrt{10}*2\sqrt{10}+3\sqrt{10}*2\sqrt{10})}$

$\tt{\implies 2(6\sqrt{100}+4\sqrt{100}+6\sqrt{100})}$

$\tt{\implies 2(6*10+4*10+6*10)}$

$\tt{\implies 2(60+40+60)}$

$\tt{\implies 2*160}$

$\tt{\implies 320m^2}$

• Now calculate total cost of painting of outer surface area of cuboid by substituting value:-]

$\sf{\implies Total\:_{(cost)}=Area\:_{(L.S.A)}*Rate}$

$\sf{\implies Total\:_{(cost)}=320*10}$

$\sf{\implies Total\:_{(cost)}=Rs.3200}$

$\sf\large{Hence,}$

$\sf{\implies Total\:cost\:of\: painting_{(outer\: surface)}=Rs.3200}$