Harder problems combine formulas. To find the radius of a sphere with volume 2304π cm³, set ⁴⁄₃πr³ = 2304π, divide by π and multiply by ¾: r³ = 1728, so r = 12 cm.
When a solid is melted and recast, the volume stays the same. A metal sphere melted into a cylinder: set the two volume formulas equal and solve for the unknown. A frustum is a cone with the top cut off: its volume is the big cone minus the small cone.
Worked example
A cone has radius 12 cm and vertical height 5 cm. Find its slant height.
- l² = 12² + 5² = 144 + 25 = 169.
- l = √169.
Answer:13 cm
Key words
- recast
- melt and reshape: volume is kept
- frustum
- a cone with its top cut off
- cube root
- undoes cubing
Practise this
New questions every time.
Common Core-referenced: HSG-GMD.A.3