Question

find the height of a cylindrical whose diameter is 42cm and the area of its curved surface is 11,880sq.cm​

Answer 1

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Area of curved surface of cylindar = $2 \pi rh$

also, = $11,800cm^{2}$

$d= 42cm \\ r = \frac{d}{2} \\ r = \frac{42}{2} \\ r = 21cm$

$11800 cm^{2} = 2 \times \frac{22}{7} \times 21 \times h \\ = > 11800cm^{2} = 2 \times 22 \times 3 \times h \\ = > 11800cm^{2} = 132 \times h \\ = > h = \frac{11800}{132} \\ = > h = 89.4cm$

Hence, the height is 89.4 cm

Answer 2

Given :-

Diameter of the cylinder = 42 cm

Curved surface area of the cylinder = 11880 cm²

To Find :-

The height of the cylinder.

Analysis :-

Firstly, we've to find the radius by dividing the diameter by two.

Consider the height as a variable.

Substitute the values we're given with in the formula of CSA of cylinder and find the value of the height accordingly.

Solution :-

We know that,

• CSA = Curved surface area
• d = Diameter
• r = Radius
• h = Height

Finding radius,

$\underline{\boxed{\sf Radius=\dfrac{Diameter}{2} }}$

Given that,

Diameter (d) = 42 cm

Substituting their values,

Radius = 42/2

= 21 cm

By the formula,

$\underline{\boxed{\sf Curved \ surface \ area \ of \ cylinder=2 \pi rh }}$

Given that,

CSA = 11880 cm²

Radius (r) = 21 cm

Let the height be 'h'.

Substituting their values,

11880 = 2 × (22/7) × 21 × h

11880 = 44 × 3 × h

11880 = 132h

By transposing,

h = 11880/132

h = 90 cm

Therefore, the height of the cylinder is 90 cm.