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If the given solid metallic right circular cone is melted and recast into a right circular cylinder having the same radius, what would be the height of this cylinder? I. The sum and product of the radius and height of the cone are 31 cm and 147 cm2 respectively. II. Total surface area of the cone is 550 cm2.

If the given solid metallic right circular cone is melted and recast into a right circular cylinder having the same radius, what would be the height of this cylinder? I. The sum and product of the radius and height of the cone are 31 cm and 147 cm2 respectively. II. Total surface area of the cone is 550 cm2. Correct Answer The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

Formula:

Total surface are of the cone = πr (l + r)

Calculation:

Let radius and height of the cone be r cm and h cm respectively.

From statement I,

(r + h) = 31 cm      ----(i)

rh = 147 cm2      ----(ii)

From equation (1) and equation (2) we can find the value of r and h,

∵ Cone is melted and recast into cylinder

⇒ Volume of cone = Volume of cylinder

⇒ 1/3 × πr2h = πr2H                         (radius is equal, H = height of cylinder)

⇒ H = h/3

∴ Data given in statement I alone is sufficient to answer. 

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