Mensuration Test

Result

Mensuration Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

If the length, breadth, height and total surface area of a cuboid are l, b, h and S, respectively, then which of the following relationships is true?

A
S = 2[lb + bh + lh]

B
S = 2[lb - bh + lh]

C
S = 2[lh + bh - lb]

D
S = 2h(l + b)

Solution

Surface area of a cuboid is equal to the sum of areas of all its faces.
All the six faces of a cuboid are rectangular in shape.
Area of front face = length × breadth
= l × h [∵ h is the breadth of the front face]
= lh

Similarly, area of back face = lh
Area of left face = h × b = hb
Area of right face = hb = hb
Area of top face = lb
Area of bottom face = lb

Now,
Surface area of cuboid = Sum of area of all the six faces
= lh + lh + hb + hb + lb + lb
= 2lh + 2hb + 2lb
= 2(lh + hb + lb)
Question 2
1 / -0

If the volume of a cube is (12)³ m³, then the total surface area of the cube is equal to

A
144 m²

B
576 m²

C
432 m²

D
864 m²

Solution

Volume of a cube = a³, where 'a' is the edge of the cube.
Given, volume of the cube = (12)³ m³
a³ = (12)³ m³

Taking cube root, we get
a = 12 m

Now, total surface area of the cube = 6a²
= 6(12)²
= 6 × 12 × 12
= 6 × 144
= 864 m²