Question

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

Answer 1

Answer:

A cylinder's volume is given by the formula:

V=\pi r^2hV=πr

2

h

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

\begin{gathered}V=\pi r^2h\\\\=\pi \times (7/2)^2\times 14\\\\=171.5\pi\end{gathered}

V=πr

2

h

=π×(7/2)

2

×14

=171.5π

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:

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

V=πr

2

h

171.5π=πr

2

×5

171.5=5r

2

r=

171.5/5

=5.857 cm

Hence, the radius of the big cylinder is 5.857 cm

Step-by-step explanation:

$hope \: it \: helps \: you$