Conversion of solids: melting and recasting sheet5-mark answer frameA solid metal hemisphere of radius 9 cm is melted and recast into small cones, each of radius 3 cm and height 3 cm. How many cones are made?
How to lay out the answer. Follow the frame, then write it in your own words.
- 1 · Write what is given and what is to be found Hemisphere: R = 9 cm. Each cone: r = 3 cm, h = 3 cm. To find: the number of cones.
- 2 · Draw the figure Draw the hemisphere with its radius 9 cm marked, and one small cone with radius 3 cm and height 3 cm.
- 3 · Write the formula Number of cones = volume of hemisphere ÷ volume of one cone = (2/3)πR³ ÷ (1/3)πr²h.
- 4 · Volume of the hemisphere
- (2/3)π × 9³ = (2/3)π × 729
- = 486π cm³
- 5 · Volume of one cone
- 6 · Divide
- 7 · Check and box the answer 54 cones. π cancels, so its value was not needed. Check: 54 × 9π = 486π.
Scoring tip: Keep π as π and cancel it. You save time and avoid rounding errors.
