Question

Find the height of right circular cylinder if it is curved surafce area is 176sq.cmand radius of base is4cm

Answer 1

$\huge \colorbox{orange}{Correct \:Question :-}$

Find the height of right circular cylinder if it is curved surface area is 176 sq.cm and radius of base is 4cm.

$\huge \colorbox{orange}{Given :-}$

⇒ Curved Surface Area of a right circular cylinder = 176 cm²

⇒ Radius of Base = 4 cm

$\huge \colorbox{orange}{To \: Find  :-}$

⇒ The height of right circular cylinder .

$\huge \colorbox{orange}{Solution:-}$

⇒ As we know that ,

${\bf{\blue{\fbox{\underline{\color{red}{Curved\:Surface\:Area\: = 2\pi rh }}}}}}$

$\sf Curved \: Surface\:Area \: = 2\pi rh$

⇒ Let the height be x

$176\:cm^{2} \: = \: 2 \times \frac{22}{7} \times x \times 4\\\\176\:cm^{2} = \frac{2 \times 22 \times x \times 4 }{7} \\\\176\: cm^{2} = \frac{176x}{7} \\\\ \frac{176 \times 7}{176} = x$

$x = 7$

$\huge{\orange{\boxed{\boxed {\boxed{\purple{\underline{\underline{\red{\mathfrak{ radius \: of \: base \: = 7 }}}}}}}}}}$

Answer 2

★Given:-

• CSA of cylinder = 176cm²
• Radius of base = 4cm

★To find:-

• The height of cylinder.

★Solution:-

We know,

✦CSA(cylinder)= 2πrh

Where,

r = radius

h = height

Putting the values,

→ CSA = 2×(22/7)×4×h

→ 176 = 2×(22/7)×4×h

→ 176 × 7 = 44×4×h

→ 1232 = 176 × h

→ h = 1232 / 176

      = 7cm.

Therefore,

Height of cylinder is 7cm.

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Know more:-

✦Total surface area of cylinder:

• TSA = 2πr(r+h)sq.units

✦Volume of a cylinder:

• V = πr²h

✦Some properties of cylinder:

• A cylinder has two parallel circular bases and a curved surface.
• The bases are always congruent and parallel.
• A cylinder does not have any vertices.
• The line segment joining the center of two circular bases is the axis of the cylinder.

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