Question

A cone has a base diameter of 14 cm and a slant height of 25 cm find its height​

Answer 1

Given :

• base diameter of cone, d = 14 cm
• so, radius of cone, r = 14/2 = 7 cm
• slant height of cone, l = 25 cm

To find :

• height of cone, h = ?

Knowledge required :

Pythagoras theorem

The Pythagoras theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of other two sides of right triangle.

Solution :

In a right circular cone ( as given in figure attached )

→ (slant height)² = (radius)² + (height)²

→ l² = r² + h²

[putting known values]

→ ( 25 )² = ( 7 )² + h²

→ h² = 625 - 49

→ h² = 576

→ h = 24 cm

therefore,

Height of cone is 24 cm .

Answer 2

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

A cone has a base diameter of 14 cm and a slant height of 25 cm. Find its height.

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

➡ The height of the cone is 24 cm.

$\mathtt{\huge{\underline{\blue{Solution:-}}}}$

$\mathcal{\large{\underline{\underline{Given:-}}}}$

• The base diameter of cone = 14 cm.

So, radius r is 14/2 = 7cm.

• A slant height of 25 cm.

$\mathcal{\large{\underline{\underline{To\:Find:-}}}}$

• The height of the cone.

$\mathcal{\large{\underline{\underline{Calculation:-}}}}$

According to the question,

• The base diameter of cone = 14 cm.

So, Radius = 14/2 =7 cm.

• A slant height of 25 cm.

Using the Pythagoras theorem ,

$\mathtt{\underline{\orange{Pythagoras\:Theorem:-}}}$ It states that the sum of the square of the base & perpendicular is the sq. of its hypotenuse.

l² = h² + r²

➡ h² = l² - r²

➡ h² = (25)² - (7)²

➡ h² = 625 - 49

➡ h² = 576

➡ h = √576

➡ h = 24 cm.

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