Question

the height of a cone is 16 cm and slant height is 20 cm find radius​

Answer 1

Answer:

The radius of the cone is 12 cm.

Step-by-step explanation:

Given information:

The height of the cone is 16 cm.

The slant height of the cone is 20 cm.

Concept Used:

Pythagoras's theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Step 1:

In $\triangle{ABC}$,

$AC^2=AB^2+BC^2\\20^2=16^2+BC^2\\BC^2=400-256\\BC=\sqrt{144}\\=12\, \text{cm}$

Hence, the radius of the cone is 12 cm.

Answer 2

According the question:-

The height of the cone is 16 cm.         ( given)

The slant height of the cone is 20 cm.   ( given)

Now we have to find out the radius of the cone.

In this sum, we have to use The Pythagoras theory.

Pythagoras's theorem = “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

 In ΔABC  ∠abc  a right angle.

∴ ΔABC becomes a right-angled triangle, whose hypotenuse = AC, AB = is perpendicular on point B. and BC = base.

In ΔABC,

AC² = AB² + BC²

20² =16² + BC²

400 - 256 = BC²

144 = BC²

BC = √144 = 12CM

∴The radius of the cone will be 12cm.

Ans :- The radius of the cone will be 12cm.

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