Q14 of 24 Page 227

The curved surface area of a right circular cone is √5 times of its base area. Let us write the ratio of the height and the length of a right circular cone are always the three sides of a right-angled triangle.

Given: Curved Surface Area of a right circular cone = √5 Base Area of right circular cone


Curved Surface Area of a right circular cone = πrl


Base area of right circular cone, A = πr2



……………….eq(i)


Now from the cone we know that,


……………..eq(ii)


Where, h is the height of cone


Now from (i) and (ii), we get that




Now, h cannot be negative, hence such cone is not possible.


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Let us fill in the blanks:

(i) AC is the hypotenuse of a right-angle triangle ABC, the radius of the right circular cone formed by revolving the triangle once around the side AB as the axis is___


(ii) If the volume of a right circular cone is V cubic unit and the base area is A sq. unit, then its height is____


(iii) The lengths of the base radii and the heights of a right circular cylinder and a right circular cone are equal. The ratio of their volume is_____.

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The height of a right circular cone is 12cm. and its volume is 100 π cm3. Let us write the length of the radius of the cone.

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The numerical values of the volume and the lateral surface area of a right circular cone are equal. If the height and the radius of the cone are h unit and r unit respectively, then let us write the value of .