What is the ratio of the sum of volumes of two-cylinder of radius 1 cm and height 2 cm each
to the volume of a sphere of radius 3 cm?
Need help with this question, the answer I keep getting is 1:9
ʏʀʀ ɪꜱꜱᴇ ɪ'ᴅ ᴘᴀꜱꜱ_ᴡᴏʀᴅ ʏᴀᴀᴅ ɴʜɪ ᴀʀʜᴀ ᴛ_ᴛ
Answers
Given :
Radius of two cylinders are 1 cm each and height are 2 cm each.
Radius of sphere = 3cm.
To find :
Ratio of the sum of volumes of two cylinder to the volume of sphere.
Solution :
∵ Volume of cylinder = πr²h
∵ Volume of sphere = 4/3 πr³
∴ Sum of volumes of two cylinders = 2(22/7 × 1² × 2)
= 2(22/7 × 1 × 2)
= 2(44/7)
= 88/7 cm³
∴ Volume of sphere = 4/3 × 22/7 × 3³
= 4/3 × 22/7 × 27
= 792/7 cm³
∴ Ratio = 88/7 : 792/7
= 88/7 × (7/792)
= 88/792
= 1/9
= 1 : 9
∴ Required ratio = 1 : 9
Given
- Radius of two cylinders = 1 cm
- Height of two cylinders = 2 cm
- Radius of sphere = 3 cm
To find
- Ratio of the sum of volumes of cylinders to volume of sphere
Solution
Volume of cylinder = πr²h
- (22/7 × 1² × 2)2
2 - Since there are two cylinders.
- 22/7 × 1 × 2 × 2
- 44/7 × 2
- 88/7
Hence, the sum of volumes of two cylinders is 88/7 cm³
Volume of sphere = 4/3πr³
- 4/3 × 22/7 × 3³
- 4/3 × 22/7 × 27
- 792/7
Hence, the volume of sphere is 792/7 cm³
Ratio (Sum of volumes of two cylinders and volume of sphere) :-
- 88/7 : 792/7
- 88/7 ÷ 792/7
- 88/7 ÷ 7/792
- 88/792
- 1/9
- 1 : 9
Hence, the ratio is 1 : 9