A cone has a height of 15 cm. If its volume is 1570 cm3, find the radius of the base.
Answer: 13 × 3.14 × r2 × 15 = 1570 ⇒ 15.7r2 = 1570 ⇒ r2 = 100 ⇒ r = 10 cm.
Step-by-step solution
Given: h = 15 cm; V = 1570 cm3
To find: Radius r
To find: Radius r
Idea: Put the known values into V = 13πr2h and solve for r. 1570 is a multiple of 3.14, so π = 3.14 is the natural choice.
- 1570 = 13 × 3.14 × r2 × 15 = 3.14 × 5 × r2 = 15.7r2.1 mark
- r2 = 1570 ÷ 15.7 = 100, so r = 10 cm.1 mark
Radius = 10 cm.
Check: 13 × 3.14 × 100 × 15 = 3.14 × 500 = 1570 ✓.
Answer to write in the exam
13πr2h = 1570
13 × 3.14 × r2 × 15 = 1570
15.7r2 = 1570 ⇒ r2 = 100
∴ r = 10 cm
Common mistakes that cost marks
- Forgetting the 13 and getting r2 = 33.3.
- Stopping at r2 = 100 and writing r = 100.
How this can come in the exam
MCQ (1 mark)
A cone of height 9 cm has volume 48π cm3. Its radius is
- 16 cm
- 4 cm
- 3 cm
- 8 cm
Show answer
(B) 4 cm
13πr2 × 9 = 3πr2 = 48π ⇒ r2 = 16 ⇒ r = 4 cm.
Try one yourself
A cone of radius 3 cm has volume 65.94 cm3. Find its height. (π = 3.14)
Show answer
13 × 3.14 × 9 × h = 9.42h = 65.94 ⇒ h = 7 cm.
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