Question

The interior of a building is in the form of a cylinder of base radius 12 m and height 3×5 m surmounted by a cone of equal base and slant height 14 m. Find the internal curved surface area of the building.

Answer 1

Step 1: Find the curved surface area (CSA) of the cylinder For a cylinder: \[ \text{CSA} = 2\pi r h, \] where $r = 12 \, \text{m}$ and $h = 3.5 \, \text{m}$: \[ \text{CSA (cylinder)} = 2\pi (12)(3.5) = 84\pi \, \text{m}^2. \] Step 2: Find the CSA of the cone  For a cone: \[ \text{CSA} = \pi r l, \] where $r = 12 \, \text{m}$ and $l = 14 \, \text{m}$: \[ \text{CSA (cone)} = \pi (12)(14) = 168\pi \, \text{m}^2. \] Step 3: Total CSA of the building  \[ \text{Total CSA} = \text{CSA (cylinder)} + \text{CSA (cone)} = 84\pi + 168\pi = 252\pi \, \text{m}^2. \] Correct Answer: $252\pi \, \text{m}^2$.