The diagram is a portion of a right circular solid cylinder of radius 7 cm and height 15 cm. The centre of the base of the cylinder is Q, while that of the top is B, where (stackrelfrown{ABC} = stackrelfrown{PQR} = 120°). Calculate, correct to one decimal place:
(a) The volume
(b) the total surface area of the solid. [Take (pi = frac{22}{7})].
Explanation
(a) Area of the major sector = (frac{theta}{360°} times pi r^{2})
= (frac{360 – 120}{360} times frac{22}{7} times 7 times 7)
= ((frac{2}{3} times 154) cm^{2})
Volume = (text{Area of the major sector} times text{height (cross section)})
= (frac{2}{3} times 154 times 15 = 1540 cm^{3})
(b) Curved surface area = (frac{240}{360} times 2pi rh)
= (frac{240}{360} times 2 times frac{22}{7} times 7 times 15)
= (440 cm^{2})
Area of rectangular surface = (2 times l times b)
= (2 times 7 times 15 = 210 cm^{2})
Area of top and bottom of cylinder (major sector)
= (2 times frac{240}{360} times frac{22}{7} times 7 times 7)
= (205.33 cm^{2})
(therefore text{Total surface area} = 440 + 205.33 + 210 = 855.33 cm^{2})