Question

a rectangle strip of aluminum 30 cm long and 10 cm wide is rolled into the form of a cylinder which would have the greater volume a cylinder 10 cm high with circumference of 30 cm or a cylinder 30 cm high with circumference of 10 cm

Answer 1

Answer:

The circumference is 30 cm (length of paper)

Height is 10 cm (width of the paper)

Circumference =2*pie*radius

Therefore- 30= 2*22/7*r

30*7= 44 r

Radius =270/44=4.7

Volume(v)=pie*square of radius*height

Volume(v)=22/7*(4.7)whole square*10

Volume(v)=695.25

Answer 2

Given :

A rectangle strip of aluminum 30 cm long and 10 cm wide is rolled into the form of a cylinder

To Find:

Which would have the greater volume a cylinder 10 cm high with circumference of 30 cm or a cylinder 30 cm high with circumference of 10 cm

Solution:

Case 1:

Height of cylinder = 10 cm

Circumference of cylinder = 30 cm

Circumference of cylinder = $2 \pi r h$

So, $2 \pi r h = 30\\2 \times 3.14 \times r \times 10 = 30\\r = \frac{30 }{2 \times 3.14 \times 10}\\r=0.47$

Volume of cylinder = $\pi r^2 h = 3.14 \times 0.47^2 \times 10=6.93626 cm^3$

Case 2:

Height of cylinder = 30 cm

Circumference of cylinder = 10 cm

Circumference of cylinder = $2 \pi r h$

So, $2 \pi r h = 10\\2 \times 3.14 \times r \times 30 = 10\\r = \frac{10}{2 \times 3.14 \times 30}\\r=0.053$

Volume of cylinder =$\pi r^2 h = 3.14 \times 0.053^2 \times 30= 0.264 cm^3$

So, a cylinder 10 cm high with circumference of 30 cm has high volume .