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

1. Calculate the volume of the standard tin:

   • The volume of a cylinder is given by the formula:

   $V = ext{Base Area} imes ext{Height} = ext{Area of circular base} imes ext{Height}$

   Given the standard tin has a radius (r) of 10 cm:

   V_{standard} = rac{22}{7} (10^2) h

   Simplifying,

   V_{standard} = rac{2200}{7} h

2. The volume of the large tin is 50% more than that of the standard tin:

   V_{large} = V_{standard} imes 1.5 = rac{2200}{7} h imes 1.5 = rac{3300}{7} h

3. Let the radius of the large tin be R:

   V_{large} = rac{22}{7} R^2 h

4. Equating both volumes:

   rac{3300}{7} h = rac{22}{7} R^2 h

5. Canceling h and rearranging gives:

   $$$$

ightarrow R = ext{sqrt}(150) ightarrow R ext{approximately } 12.25 ext{ cm}$$

Thus, the radius of the large tin is approximately 12.25 cm.