Question

the diameter of the two circular ends of the bucket are 44cm and 24cm.the height of the bucket is 35cm. find the volume of the bucket

Answer 1

Given the height of the bucket = 35cm.

Given the diameter of 1 circular end of bucket = 44 cm, Then the radius r = 22cm.

Given the diameter of another end = 24 cm, Then the radius r = 12 cm.

We know that Volume of the bucket = 1/3pir^2h

                                                            = 1/3 * 22/7 * ((22)^2 + (12)^2 + 22 * 12) * 35

                                                            = 35/3 * 22/7 * (484 + 144 + 264)

                                                            = 35 * 22 * 892/3 * 7

                                                            = 32706.6 cm^3
 
                                                            = 32.7 litres.


The volume of the bucket = 32.7 L.


Hope this helps!

Answer 2

Given: Diameter of two circular ends of a bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm.

Bucket is in the shape of frustum.

Let V be the Volume of the Bucket(Frustum)

Volume of the frustum is given by:

× h × (R2 + r2 + Rr) (here r and R are the radii of smaller and larger circular ends respectively)

∴ V =

× h × (R2 + r2 + R × r)

⇒ V =

× 35 × (222 + 122 + 22 × 12) (diameters are 44 and 24 cm, ∴ their radii are 22cm and 12cm respectively)

⇒ V =

× 35 × (484 + 144 + 264) =

× 35 × (892)

⇒ V =

× 35 × (892) = 32706.6 cm3 = 32.7 litres (∵ 1000cm3 = 1 litre)

∴ The capacity of the bucket is: 32.7 litres