Question

The height of a right circular cone whose radius is 3cm and slant height is 5cm will be

Answer 1

Answer:

• Height of cone is 4 cm.

Step-by-step explanation:

Given :-

• Radius of right circular cone is 3 cm.
• Slant height of right circular cone is 5 cm.

To find :-

• Height of right circular cone.

Solution :-

We know,

• $\sf l = \sqrt{ {r}^{2} + {h}^{2} }$

By this,

• $\sf h = \sqrt{ {l}^{2} - {r}^{2} }$

Where,

• l is slant height, h is height and r is radius of cone.

Put the values :

$\sf \longrightarrow h = \sqrt{ {(5)}^{2} - {(3)}^{2} }$

$\sf \longrightarrow h = \sqrt{25 - 9}$

$\sf \longrightarrow h = \sqrt{16}$

$\sf \longrightarrow \boxed{ \bold{h = 4}}$

Therefore,

Height of cone is 4 cm.

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More formulas of cone✽ :

• Total surface area of cone is πr² + πrl.

• Volume of cone is 1/2 πr²h

• Lateral surface area of cone is πrl

In above formulas r is radius, h is height and l is slant height of cone.

Answer 2

Answer :-

Height = $4 \: cm$

Step-by-step explanation

GIVEN :-

• Radius of a right circular cone = 3cm
• Slant height of a right circular cone = 5cm

TO FIND :-

• Height of the right circular cone

FORMULA USED :-

$height \: = \sqrt{ {(slant \: height)}^{2} - {(radius)}^{2} }$

SOLUTION :-

Let,

'h' = Height of the right circular cone

'r' = Radius of a right circular cone

'l' = Slant height of a right circular cone

According to the question :-

$height \: = \sqrt{ {(slant \: height)}^{2} - {(radius)}^{2} } \\ ⟹ \: h \: = \sqrt{ {(l)}^{2} - {(r)}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ \: h = \sqrt{ {5}^{2} - {3}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ \: h = \sqrt{25 - 9} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ \:h = \sqrt{16} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ \: h = 4 \: cm \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

RELATED FORMULAS TO CONE

$✰ \: curved \: surface \: area = \pi \: rl \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ✰ \: area \: of \: circular \: base \: = \pi \: {r}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ✰ \: total \: surface \: area \: = \: \pi \: rl \: + \pi {r}^{2} \: \: \: \: \: \: \\ ✰ \: lateral \: surfce \: area \: = \pi \: r \: \sqrt{ {h}^{2} + {r}^{2} } \\ ✰ \: slant \: height \: = \sqrt{ {h}^{2} + {r}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Here,

$h = height \: of \: the \: cone \: \: \: \: \: \: \: \: \: \: \: \\ l = slant \: height \: of \: the \: cone \\ r = radius \: of \: the \: cone \: \: \: \: \: \: \: \: \: \: \:$