Answer to Question #195830 in Geometry for help !!

Question

Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).

Answer 1

$Solution: For ~this~ case ~what~ we~ should~ do~ is~ model~ the ~soda ~can ~as~ a ~cylinder. \\We have then: \\V=\pi r^2 h \\Where, \\r: radius ~ of ~the ~can \\h: height ~of ~the ~can \\From ~`here, we ~clear~ the ~value ~of ~the ~height: \\Substituting ~values~ we~ have: \\We~ are~ now~ looking~ for~ the~ volume ~of ~the ~cone. \\We ~have~ then: \\V=\frac{1}{3} \pi r^2 h \\Substituting~values~we~have: \\V=\frac{1}{3} \pi (2^2) (2.87)=12.02 \approx 12 \\Answer:The~volume ~of~ a ~cone~ that~ fits~ perfectly~ inside~ the~ soda~ can~ is ~V=12$