Question

the curved surface area of a right circular cylinder is 4.4sq cm. If the radius of the base is 0.7cm then the height of the cylinder is ​

Answer 1

• Height of cylinder is 1 cm.

Step-by-step explanation:

Given :-

• Curved surface area of a right circular cylinder is 4.4 cm².
• Radius of base is 0.7 cm.

Solution:-

Let, Height of cylinder be h.

Diagram of cylinder :-

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){1}{\sf{0.7cm}}\put(9,17.5){\sf{h}}\end{picture}$

Now,

$\boxed{\sf \bold{Curved\: surface \: area = 2\pi r h}}$

Where,

• r is base radius of cylinder and h is height of cylinder.

Put, Curved surface area and radius of cylinder in formula:

$\sf \longrightarrow 4.4 = 2 \times \dfrac{22}{7} \times 0.7 \times h$

$\sf \longrightarrow 4.4 = \dfrac{44}{7} \times 0.7 \times h$

$\sf \longrightarrow 4.4 = \dfrac{30.8}{7} \times h$

$\sf \longrightarrow 4.4 \times 7 = 30.8 \times h$

$\sf \longrightarrow 30.8 = 30.8 \times h$

$\sf \longrightarrow h = \cancel{\dfrac{30.8}{30.8} }$

$\sf \longrightarrow \pink{ \boxed{ \sf \bold{h = 1}} \star}$

Verification:-

$\sf \longrightarrow 4.4 = 2 \times \dfrac{22}{7} \times 0.7 \times h$

• Put h = 1

$\sf \longrightarrow 4.4 = 2 \times \dfrac{22}{7} \times 0.7 \times 1$

$\sf \longrightarrow 4.4 = \dfrac{44}{7} \times 0.7$

$\sf \longrightarrow 4.4 = \dfrac{30.8}{7}$

$\sf \longrightarrow 4.4 = 4.4$

$\boxed{\sf Hence \: Verified.}$

Therefore,

Height of cylinder is 1 cm.

Answer 2

Answer:

Given :-

• A curved surface area of a right circular cylinder is 4.4 cm².
• The radius of the base is 0.7 cm.

To Find :-

• What is the height of the cylinder.

Formula Used:-

$\boxed{\bold{\large{C.S.A\: =\: 2{\pi}rh}}}$

where,

• C.S.A = Curved surface area
• r = radius
• h = height

Solution :-

Let, the height of a cylinder be h

$\sf Given \begin{cases} & \sf{C.S.A\: of\: a\: cylinder = \bf{4.4\;c{m}^{2}}} \\ & \sf{Radius = \bf{0.7\;cm}} \end{cases}$

According to the question by using the formula we get,

⇒ $4.4\: =\: 2 \times \dfrac{22}{7} \times 0.7 × h$

⇒ $4.4\: =\: \dfrac{30.8}{7} \times h$

⇒ $4.4\: =\: 4.4\: \times h$

⇒ $h\: =\: \sf\dfrac{\cancel{4.4}}{\cancel{4.4}}$

➠ h = 1

$\therefore$ The height of the cylinder is 1 cm .