Question

A right circular cone has a slant height 3 times the radius of the base. If the area of the curved surface of the cone is 18 cm^2, find the diameter of the base

Answer 1

Step-by-step explanation:

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Answer 2

Given:

We have given the slant height of cone is 3times radius of base. And the  curved surface of the cone is 18.

To Find:

We have to  find the diameter of the base?

Step-by-step explanation:

• Let the radius of base of cone be xcm
• Then according to the question slant height is three times the base of radius
• Hence, the slant height is 3x
• Now we have the Curved surface area of cone is 18 square.cm
• We know curved surface area of cone is given by the formula

       $\textrm{Curved surface area of cone}=\pi rl$

• Where r is the radius=x, l is the slant height 3x Put these value in above equation we get

      $18=\pi x\times3x$

• Now simplify the above equation

       $18=\frac{22}{7} \times x\times3x\\3x^2=\frac{18\times7}{22} \\x^2=\frac{126}{66} \\x^2=\frac{63}{33}=\frac{21}{11} \\x=\sqrt{\frac{21}{11} }$

• Hence the diameter is given by 2 times the radius

Hence, the diameter is $2\sqrt{\frac{21}{11} }$.