Percy sells paint in standard tins and large tins - OCR - GCSE Maths - Question 18 - 2018 - Paper 1

To determine the radius of the large tin, we first calculate the volume of the standard tin:
The formula for the volume of a cylinder is given by:
$V = ext{Area}_{ ext{base}} imes ext{height}$
Assuming both tins have the same height, the volume of the standard tin is:
$V_s = ext{Area} = ext{base radius}^2 imes h = ext{10}^2 imes h = 100h$
The volume of the large tin is:
$V_l = V_s + 0.5V_s = 1.5V_s = 1.5(100h) = 150h$
For the large tin, let the radius be r. Thus,
$V_l = r^2 imes h$
Setting the volumes equal gives:
$150h = r^2 imes h$
This implies:
$r^2 = 150$
Thus,
r = rac{ ext{sqrt}(150)}{1} ext{ cm} \\ r ext{ is approximately } 12.247 ext{ cm.}