The diameter of the base of a right circular cylinder is 14 cm, while its length is 40 cm. Find the total surface area of the cylinder.?

Given, r = 7 cm, h = 80 cm
Volume = ?r²h = (22/7) x 7 x 7 x 80
= 12320 cm³

Here, k = 12%
According to the formula,
Percentage increase in volume = [(1 + k/100)³ - 1] x 100%
= [(1 + 12/100)³ - 1] x 100%
= [(1.12)³ - 1] x 100%
= 0.404928 x 100% = 40.4928%

Here, x = y = -19%
According to the formula,
Percentage decrease in surface area
= [x + y + xy/100]%
= [- 19 - 19 + (-19) x (-19) /100]%
=[-38 + 361/100]%
= [-38 + 3.61]% = -34.39 %

Let the edge of a square be x. and sum of its edges = 12 x
Now, by condition, x³ = 12x
? x(x² - 12) = 0
? Its total surface area = 6x² = 6(12) = 72 sq units

Volume of the cuboid = 720 cm³

Height of the cuboid = Volume of the cuboid / Base area of the cuboid
= 720 / 72 = 10 cm [By Hit Trail]

Surface area of the cuboid = 2 (lb + bh + hl)
= 2(9 x 8 + 8 x 10 + 10 x 9 )
= 2 (72 + 80 + 90)
= 2 x 242
= 484 cm²

? It is obvious that length, breadth and height of the cuboid is 9 cm, 8 cm and 10 cm.

Given, lateral surface area = 94.2 sq cm
? 2?rh = 94.2
? r = 94.2/(2?h) = 94.2/(2 x 3.14 x 5) = 3 cm

Given, r₁ = 1 cm, h₁ = 30 cm, h₂ = 300 cm.
Volume of rod = Volume of wire
? ?r₁²h₁ = ?r²₂h₂
? ? x (1)² x 30 = ? x r²₂ x 300
? r²₂ = 30/300
? r₂ = 1/?10 cm
? diameter = 2r₂
= 2 x 1/?10 = 2/?10cm.

Let the height and radius and radius of solid cylinder be h and r cm respectively
Given that, radius (r) = 5 cm
and total surface area = 660 cm²
? 2?rh + 2?r² = 660
? 2?r(h + r) = 660
? (h + 5) = 330/5? = 330/5 x 7/22
? h = 66 x (7/22) - 5 = 21 - 5
? Required height = 16 cm

Curved surface area of the cylinder = 2?rh
= 2 x (22/7) x 7 x 160
= 7040 sq cm

Let radii be 2r and 3r and heights be 5h and 3h.
? Ratio of volumes = [?(2r)² x 5h] / [?(3r)² x 3h]
= 20/27 = 20 : 27