Mensuration Test - 4

Total surface area of cylinder = 2πr (r + h) ... (1)
'r' is the radius and 'h' is the height of the cylinder.

Given, radius = b
Height = a

Putting these in (1), we get

Total surface area = 2πb (b + a)
or 2πb (a + b)

Given, length = 10 cm
Height = 15 cm

Lateral surface area = 1200 cm²
b = ?

We know, lateral surface area = 2h (l + b)

Therefore, 1200 = 2 × 15 (10 + b)
1200/30 = (10 + b)
10 + b = 40
b = 40 – 10
= 30 cm

Lateral surface area of a cubical box = 4a², where `a` is the edge of the box.
Given, a = 3 m
∴ Lateral surface area = 4 (3)²
= 4 × 9
= 36 m²

Given, Length of cuboid (l) = 6 cm
Breadth of cuboid (b) = 8 cm
Height of cuboid (h) = 7 cm

Total surface area of cuboid = 2 (lb + bh + lh)
= 2 (6 × 8 + 8 × 7 + 6 × 7)
= 2 (48 + 56 + 42)

= 2 (146)
= 292 cm²

If 'a' is the edge of the cube, then total surface area = 6a²
96 = 6a²

96/6²
16 = a²

a = 4 cm [∵ length is always positive.]

Then volume = a³

= (4)³ = (4 × 4 × 4) cm³
= 64 cm³