Question 4 of 13intermediate🔧 ApplyNumerical3 marks
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
(i)
Answer
The greatest diameter of the hemisphere is 7 cm.
(ii)
Answer
The surface area of the solid is 332.5 cm².
Explanation
This question is similar to Example 2 from the textbook. The hemisphere is placed on top of the cube, so its maximum diameter cannot exceed the side of the cube. For surface area, we follow the formula: Surface area of solid = TSA of cube – base area of hemisphere + CSA of hemisphere. Note that the base area of the hemisphere is subtracted because that portion of the cube's top face is covered by the hemisphere.