Question

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​

Answer 1

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

Answer 2

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