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Question of The Day12-07-2021

The Semi vertical angle of a cone is, θ = cos^-10.96. If the base radius of the cone is 7 cm, the what is the volume of the cone?

Answer

Correct Answer : a ) 1232 cm²

Explanation :

According to the question

The Semi vertical angle of a cone is θ = cos^-10.96

⇒cos θ = 0.96

⇒cos θ=\({96 \over 100}={24 \over 25}\)

We know that,

cos θ\({Base \over Hypotenuse}\)

⇒ Base (AD) = 24 units

⇒ Hypotenuse = 25 units

In △ADC (Using Pythagoras theorem)

AC² = AD² + DC²

⇒ 25² = 24² + DC²

⇒ DC = 7 units

⇒ Radius of the base of cone (DC) = 7 cm

⇒ 7 units = 7 cm

⇒ Height of the cone (24 units) = 24 cm

volume of cone=\({1 \over 3}\)*πr²h

⇒ Substituting the values

⇒\({1 \over 3}*{22 \over 7}*7*7*24\)

⇒ 1232 cm²

Hence, (a) is the correct answer.

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