Question

The Curved surface area of a right circular cylinder is 4.4 sq.cm. The radius of the base is 0.7 cm. The height of the cylinder will be: *

(a) 2 cm

(b) 3 cm

(c) 1 cm

(d) 1.5 cm

.
​

Answer 1

Given :-

• CSA of a cylinder = 4.4 cm^2

• The radius of the base = 0.7 cm

Solution :-

Here,

CSA = 4.4 cm^2 , Radius = 0.7cm ,

Height = ?

Let the height be h

Now,

Using formula of CSA

CSA of cylinder = 2πrh

4.4 = 2 * 22/7 * 0.7 * h

44/10 = 2 * 22/7 * 7/10 * h

44/10 = 22 / 5 * h

h = 22/5 * 10/44

h = 2/2 = 1 cm

Hence, The height of the cylinder is 1 cm

Option ( c ) is correct .

Some important formulas :-

CSA of cylinder = 2πrh

TSA of cylinder = 2πr( r + h)

Volume of cylinder = πr^2h $.$

Answer 2

${\large{\bold{\rm{\underline{Question}}}}}$

★ The Curved surface area of a right circular cylinder is 4.4 sq.cm. The radius of the base is 0.7 cm. The height of the cylinder will be -

• (a) 2 cm

• (b) 3 cm

• (c) 1 cm

• (d) 1.5 cm

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ The Curved surface area of a right circular cylinder is 4.4 cm²

★ The radius of the base is 0.7 cm.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ Height of the cylinder.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ Height of the cylinder = 1 cm (Option c)

${\large{\bold{\rm{\underline{Using \; concepts}}}}}$

★ Formula to find CSA of cylinder.

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

★ CSA of cylinder = 2πrh

$\; \; \; \; \; \; \; \;{\sf{Where,}}$

✨ π pronounced as pi

✨ Value of π is 22/7 or 3.14

✨ r denotes radius

✨ h denotes height

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let us put the values according to the formula to find CSA of cylinder !..

☑️ CSA = 2πrh

• 4.4 = 2 × 22/7 × 0.7 × h

• 4.4 = 1.4 × 22/7 × h

• 4.4 = 14/10 × 22/4 × h

• 4.4 = 44/10 × h

• 4.4 = 4.4 × h

• 4.4 / 4.4 = h

• 1 = h

• h = 1 cm

Henceforth, height of given cylinder is 1 cm

${\large{\bold{\rm{\underline{Additional \; knowledge}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: circle = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Circumference \: of \: circle \: = \: 2 \pi r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: square \: = \: Side \times Side}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: triangle \: = \: \dfrac{1}{2} \times breadth \times height}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: paralloelogram \: = \: Breadth \times Height}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: circle \: = \: \pi b^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: triangle \: = \: (1st \: + \: 2nd \: + 3rd) \: side}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: paralloelogram \: = \: 2(a+b)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: cuboid \: = \: 2(l \times b + b \times h + l \times h}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto LSA \: of \: cuboid \: = \: 2h(l+b)}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cuboid \: = \: L \times B \times H}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diagonal \: of \: cuboid \: = \: \sqrt 3l}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Perimeter \: of \: cuboid \: = \: 12 \times Sides}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cylinder \: = \: \pi r^{2}h}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Surface \: area \: of \: cylinder \: = \: 2 \pi rh + 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Lateral \: area \: of \: cylinder \: = \: 2 \pi rh}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Base \: area \: of \: cylinder \: = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Height \: of \: cylinder \: = \: \dfrac{v}{\pi r^{2}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: cylinder \: = \:\sqrt frac{v}{\pi h}}}}$