Three metallic spheres of radii 10 cm, 8 cm, and 6 cm, respectively, are melted to form a single solid cone of radius 12 cm. Find the curved surface area of the cone, correct to two places of decimal. (Take π = 3.14)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 1864.41 cm2
Formula used
The volume of a sphere
V = 4/3 π r³, where V = volume and r = radius.
The volume of a cone
V= ⅓ 𝜋r2h cubic units, where r is the radius of the circular base and h is the height of the cone
According to the question
The volume of the three metallic spheres = Volume of the single solid cone
(4/3) * π * (103 + 83 + 63) = (1/3) * π * 122 * h
4 * 1728 = 144 * h
h = 48 cm
The curved surface area of the cone = πrl
l = √(r2 + h2)
l = √(144 + 2304) = 49.48 cm
Hence, CSA = πrl = 3.14 * 12 * 49.48 = 1864.41 cm2