Question

The small cylinder can fill
the big cylinder to a height
of 5 cm.
Work out the radius
of the big cylinder.

Answer 1

Answer:

5.857 cm

Step-by-step explanation:

A cylinder's volume is given by the formula:

$V=\pi r^2h$

-The small cylinder's dimensions are d=7, h=14, it's volume is calculated as:

$V=\pi r^2h\\\\=\pi \times (7/2)^2\times 14\\\\=171.5\pi$

We are told that this volume fills the big cylinder to a height of 5cm.

#We equate this volume to the big cylinder's 5cm and solve for r:

$V=\pi r^2h\\\\171.5\pi=\pi r^2\times 5\\\\171.5=5r^2\\\\r=\sqrt{171.5/5}\\\\=5.857 \ cm$

Hence, the radius of the big cylinder is 5.857 cm

Answer 2

The radius  of the big cylinder is 5.857 cm and this can be determined by using the formula of volume of the cylinder.

Given :

• The small cylinder can fill  the big cylinder to a height  of 5 cm.
• The diameter of the small cylinder is 7cm and the height of the small cylinder is 14cm.

First, find the volume of the small cylinder. The volume of the cylinder is given by the formula:

$\rm Volume = \pi r^2h$

where 'r' is the radius of the cylinder and 'h' is the height of the cylinder.

Now, substitute the values of the radius 'r' and height 'h' of the small cylinder in the above formula.

$\rm V = \pi \times (3.5)^2\times (14)$

$\rm V = 171.5\pi$

Now, it is given that the small cylinder can fill  the big cylinder to a height  of 5 cm that is:

$171.5\pi = \pi \times r^2 \times (5)$

$171.5=r^2 \times 5$

$\sqrt{34.3} = r$

r = 5.857 cm

For more information, refer to the link given below:

https://brainly.com/question/15861918