A toy's lower part is a hemisphere and the upper part is a cone (radius 3 cm, height 4 cm). Find the volume and the surface area of the toy. (π = 3.14)

Answer: Volume = 94.2 cm³, surface area = 103.62 cm²

Radius of hemisphere = radius of cone, \(r=3\) cm; height of cone \(h=4\) cm.

Slant height \(l=\sqrt{h^2+r^2}=\sqrt{16+9}=5\) cm.

Volume \(=\tfrac23\pi r^3+\tfrac13\pi r^2h\)

\[=\pi(18+12)=30\pi=30\times3.14=94.2\ \text{cm}^3\]

Surface area = curved surface of hemisphere + curved surface of cone

\[=2\pi r^2+\pi rl=\pi(18+15)\]

\[=33\times3.14=103.62\ \text{cm}^2\]