A four sided pyramid, with a vertical height of 10cm and the base 4cmx4cm is placed on the top of a cylinder with radius 1.5cm and a height of 15cm. What is the exposed surface area?

Bottom end of cylinder = 1.5²x pi = 7.07cm²Cylinder shaft surface area = 3 x pi x 15 = 141.4cm²Top end of cylinder exposed = 0 Base of pyramid exposed = (4 x 4) - 7.07 = 8.9cm²Sides of pyramid = (use pythagoras) sqrt(10²+2²) = 10.2cm up the face of one sideUse A=1/2 x b x h = 0.5 x 4 x 10.2 = 20.4cm² for each side so 4 x 20.4 = 81.6 cm²Total exposed surface area = 7.07 + 141.4 + 8.9 + 81.6 = 239.0 cm²