A solid hemisphere is placed on a cube of side 7 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, correct to two decimal places? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 432.83 cm3
The flat face of the hemisphere is the largest circle that fits in the top face, so its diameter equals the side of the cube. The volume of the solid is the cube plus the hemisphere, \(\frac{2}{3}\pi r^3\).
Radius of the hemisphere \(=7\div2=3.5\) cm
Cube \(=7^3=343\) cm3
Hemisphere \(=\displaystyle\frac{2}{3}\times\frac{22}{7}\times3.5\times3.5\times3.5=\frac{539}{6}\approx89.83\) cm3
Total \(\approx343+89.83=432.83\) cm3
