Multiple choice

A craftsman has blocks of three different metals: cobalt (816 cm3), nickel (1152 cm3), and zinc (624 cm3). He melts down each metal separately to cast solid closed conical objects (with base), all having the same height and a base radius of 4 cm. If the craftsman wants to minimise the total number of cones while using all the material, what is the combined surface area of all the cones (including the base), in square centimetres?

  1. 846π + 216 16 π 2 − 18

  2. 486π + 126 81 π 2 − 16

  3. 846π + 126 81 π 2 − 16

  4. 864π + 216 16 π 2 + 81

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The greatest common usable cone volume is gcd(816, 1152, 624) = 48 cm^3. This gives 54 cones, height 9/pi cm, and total surface area 864pi + 216sqrt(16pi^2 + 81) cm^2.

Keep practicing — related questions