Question

the dimensions of a
cuboid are in ratio
3:2:1 and its volume
is 10368 cm² . Find
its total surface area​

Answer 1

Given:

• Dimensions of cuboid = 3:2:1
• Volume = 10368 cm²

To find:

☞ Total Surface Area = ?

Method:

Let the sides be 2x, 3x and x

Here, the formulas of Total Surface Area and Volume of cuboid is used

Formulas used:

★ TSA = 2(lb + bh + hl)

★ Volume = l × b × h

Where,

l is the length

b is the breadth

h is the height

Since we know the Volume of cuboid, let's apply the formula of Volume first.

Volume = l × b × h

➞ Volume = (3x)(2x)(1x)

➞ Volume = 6x³

➞ 10368 = 6x³

➞ x³ = 10368 ÷ 6

➞ x³ = 1728

➞ x = ∛1728

∴ x = 12 cm

Finding the dimensions;

• Length = 3x = 3(12) = 36 cm
• Breadth = 2x = 2(12) = 24 cm
• Height = x = 12 cm

Now for finding the Total Surface Area,

TSA = 2(lb + bh + hl)

➞ TSA = 2((36 × 24) + (24 × 12) + (12 × 36))

➞ TSA = 2(864 + 288 + 432)

➞ TSA = 2(1584)

∴ TSA = 3168 cm²