A solid hemisphere is placed on a cube of side 14 cm so that its flat circular face fits exactly on the top face of the cube, touching all four edges of that face. What is the total volume of the solid? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3,462.67 cm3
The largest circle on a square face touches all four edges, so the diameter of the hemisphere equals the side of the cube. The total volume is the cube's volume \(a^3\) plus the hemisphere's volume \(\displaystyle \frac{2}{3}\pi r^3\).
Radius of the hemisphere \(=14\div2=7\) cm
Volume of the cube \(=14\times14\times14=2744\) cm3
Volume of the hemisphere \(\displaystyle =\frac{2}{3}\times\frac{22}{7}\times7\times7\times7=\frac{2156}{3}\approx718.67\) cm3
Total \(\displaystyle =2744+\frac{2156}{3}=\frac{10388}{3}\approx3462.67\) cm3
