Question

A bucket is 20cm in diameter at the open 12cm in diameter at the bottom and 16cm deep.To what depth will the bucket fill in cylindrical tin 28cm in diameter?

Answer 1

First, we need to calculate the volume of the original bucket.

Volume of a cylinder = πr^2h, where r is the radius and h is the height.

Radius of the open end of the bucket = diameter/2 = 20cm/2 = 10cm
Radius of the bottom of the bucket = 12cm/2 = 6cm
Height of the bucket = 16cm

Volume of original bucket = π(10^2)(16) - π(6^2)(16)
= 160π - 96π
= 64π cubic cm

Now, we need to calculate how much of the larger bucket will be filled to the same depth.

Radius of the larger bucket = 28cm/2 = 14cm

Volume of larger bucket filled to the same depth = 64π/π(14^2)
= 64/196
= 0.32653

Therefore, the larger bucket will be filled to a depth of approximately 32.65cm.