The Semi vertical angle of a cone is, θ = cos-1 0.96. 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-1 0.96
⇒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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