Two cuboids with equal volumes will always have equal surface areas. Is the given statement true or false

Solution:

If two cuboids have equal volumes implies that

L₁ × B₁ × H₁ = L₂ × B₂ × H₂

Where

L₁ & L₂ = Length of cuboid 1 and cuboid 2 respectively

B₁ & B₂ = Breadth of cuboid 1 and cuboid 2 respectively

H₁ & H₂ = Height of cuboid 1 and cuboid 2 respectively

However it is Not necessary that:

L₁ = L₂

H₁ = H₂

B₁ = B₂

Hence the surface area of the cuboid may not be same.

The statement is false.

✦ Try This: Two cuboids one of Length 10 cm, Breadth 4 cm and height 3 cm and the other cuboid of length = 12 cm, Breadth 5 cm and height 2 cm will have the same surface area. Is the given statement true or false

Given

L₁ = 10 cm

B₁ = 4 cm

H₁ = 3 cm

The volume of the first cuboid is = 10 × 4 × 3 = 120 cm³

Given

L₂ = 12 cm

B₂ = 5 cm

H₂ = 2 cm

The volume of the second cuboid is = 12 × 5 × 2 = 120 cm³

Hence we observe that the volumes of both cuboids are same.

Let us calculate their surface area:

Surface Area of Cuboid 1 = 2 × (L₁B₁ + B₁H₁ + L₁H₁)

= 2 × (10 × 4 + 4 × 3 + 10 × 3)

= 2 × (40 + 12 + 30)

= 2 × (82)

= 164 cm²

Surface Area of Cuboid 1 = 2 × (L₂B₂ + B₂H₂ + L₂H₂)

= 2 × (12 × 5 + 5 × 2 + 12× 2)

= 2 × (60 + 10 + 24)

= 2 × (94)

= 188 cm²

The statement is false

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

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NCERT Exemplar Class 8 Maths Chapter 11 Problem 56

Two cuboids with equal volumes will always have equal surface areas. Is the given statement true or false

Summary:

Two cuboids with equal volumes will always have equal surface areas. The statement is False

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