The surface area of a cuboid formed by joining face to face 3 cubes of side x is 3 times the surface area of a cube of side x. Is the given statement true or false
Solution:
The three cubes which are joined face to face are shown below.
If the three cubes are joined face to face, the resultant solid will be a cuboid of length 3x, breadth x and height x.
The surface area of the cuboid will be = 2[x × 3x + 3x × x + x × x]
= 2[3x² + 3x² + x²]
= 2[7x²]
= 14x²
The surface area of cube with side x = 6x²
It is evident that surface area of the resultant cuboid ≠ 3 times the surface area cube with side x
14x² ≠ 3(6x²)
Hence the statement is False.
✦ Try This: The volume of a cuboid formed by joining face to face 3 cubes of side x is 6 times the volume of a cube of side x. Is the given statement true or false
The three cubes which are joined face to face are shown below.
If the three cubes are joined face to face, the resultant solid will be a cuboid of length 3x, breadth x and height x.
The volume of the cuboid will be = 2[x × 3x × x ]
= 2[3x³]
= 6x³
The volume of cube with side x = x³
It is evident that volume of the resultant cuboid ≠ 3 times the volume of the cube with side x
6x³ = 6(x³)
Hence the statement is True
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 55
The surface area of a cuboid formed by joining face to face 3 cubes of side x is 3 times the surface area of a cube of side x. Is the given statement true or false
Summary:
The surface area of a cuboid formed by joining face to face 3 cubes of side x is 3 times the surface area of a cube of side x. The statement is false(F)
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