# The Length, Breadth, and Height of a Cuboid Are in the Ratio 5 : 3: 2. If Its Volume is 240 Cm3; Find Its Dimensions. Also, Find the Total Surface Area of the Cuboid. - Mathematics

Sum

The length, breadth, and height of a cuboid are in the ratio 5 : 3: 2. If its volume is 240 cm3; find its dimensions. Also, find the total surface area of the cuboid.

#### Solution

Let length of the given cuboid = 5x

Breadth of the given cuboid = 3x

Height of the given cuboid = 2x

Volume of the given cuboid = Length x Breadth x Height
= 5x x 3x x 2x = 30x3

But we are given volume = 240 cm3

30x3 = 240 cm3

⇒ x3 = 240/30

⇒ x3 = 8

⇒ x = 8^(1/3)

⇒ x = (2 xx 2 xx 2)^(1/3)

⇒ x = 2 cm

Length of the given cube = 5x = 5 x 2 = 10 cm

Breadth of the given cube = 3x = 3 x 2 = 6 cm

Height of the given cube = 2x = 2 x 2 = 4cm

Total surface area of the given cuboid = 2(l x b + b x h + h x l)

= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124

= 248 cm2

Concept: Surface Area of a Cuboid
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 21 Surface Area, Volume and Capacity
Exercise 21 (A) | Q 3 | Page 238