Question

a)The lateral surface area of a hollow cylinder is 5472cm²

. It is cut along

its height and formed a rectangular sheet of width 36cm. Find the

perimeter of the rectangular sheet.


b) Gopal painted the outside of the cabinet of measure 3.5m x 2.5m x 2m.

How much surface area did he cover if he painted all except the bottom of

the cabinet?​

Answer 1

Question 1 :-

Given :-

• Lateral surface area of a hollow cylinder = 5472cm²
• It is cut along it's height to form a rectangular sheet of width 36cm

Aim :-

• To find the perimeter of the rectangle

Formula to use :-

$\boxed {\sf{lateral \: surface \: area \: of \: a \: cylinder = 2 \times \pi \times r \times h}}$

$\boxed {\sf perimeter \: of \: a \: rectangle \: = 2(length + breadth)}$

• r - radius
• h - height

When a rectangle is rolled into a cylinder, the Breadth (width) becomes the height and the length becomes the circumference of the circular bases.

Here, we have to find the value of 2πr which is the length of the rectangle inorder to find it's perimeter (as we know that the perimeter of the circle = 2πr)

Substituting the values,

$\implies \sf 5472 = 2\pi r \times 36$

Transposing 36,

$\implies \sf \dfrac{5472}{36} = 2\pi r$

Reducing to the lowest terms,

$\implies \sf 152 = 2\pi r$

Now that we have the value of the length,

Perimeter of the rectangle :-

➡ 2(152 + 36)

➡ 2(188)

➡ 376cm

Question 2 :-

Given :-

• Dimensions of the cabinet = 3.5m × 2.5m × 2m

Aim :-

• To find the Total surface area to be painted excluding the bottom of the cabinet?

Formula to use :-

$\boxed { \sf area \: to \: be \: painted = [2 \times height(length + breadth)] + (length \times breadth)}$

The dimensions are Always given in the order :- Length × Breadth × Height.

Hence,

• Length = 3.5m
• Breadth = 2.5m
• Height = 2m

Substituting the values,

Area to be painted :-

$\implies \sf [2\times 2(3.5 + 2.5) ]+ (3.5 \times 2.5)$

$\implies \sf 4(6) + (8.75)$

$\implies \sf 24 + 8.75$

$\implies \sf 32.75 {m}^{2}$

Therefore the area to be painted is 32.75m²

More formulas :-

$\boxed{ \sf Lateral \: surface \: area \: of \: a \: cube = 4a^2}$

$\boxed { \sf Lateral \: surface \: area \: of \: a \: cylinder = 2\pi r h }$

$\boxed{ \sf Lateral \: surface area \: of \: a \: cuboid = 2h(l+b)}$

$\boxed { \sf Total \: surface \: area \: of \: a \: cube = 6a^2}$

$\boxed {\sf Total \: surface \: area \: of \: a \: cylinder = 2\pi r(h+r)}$

$\boxed {\sf Total \: surface \: area \: of \: a \: cuboid = 2(lb + bh + hl)}$