COMPOSITE SOLIDS Composite solids can be formed by

COMPOSITE SOLIDS Composite solids can be formed by either Ex (i) combining two or more shapes. (ii) removing one solid from another. A grain silo consists of a cylinder of diameter 6 m and height 8 m topped by a hemisphere. For both cylinder & hemisphere d = 6 so r = 3. Vol cylinder = r 2 h = 3. 14 X 3 X 8 = 226. 08 8 m Vol h-sphere = 2/3 r 3 = 2 X 3. 14 X 3 X 3 3 = 56. 52 6 m Total vol = 226. 08 + 56. 52 = 282. 6 = 283 m 3

Example A “Polo” mint is 4 mm thick with a diameter of 12 mm. The hole is 6 mm in diameter. Find the total vol of mint. 4 mm 6 mm 12 mm NB: the mint is a “big cylinder – a wee cylinder”. Big C. d = 12 so r = 6 & h = 4 V = r 2 h = 3. 14 X 6 X 4 = 452. 16 Wee C. d = 6 so r = 3 & h = 4 V = r 2 h = 3. 14 X 3 X 4 = 113. 04 Vol mint = 452. 16 – 113. 04 = 339. 12 = 339 mm 3

Find the volume of the composite solid. Use 3. 14 for π. This composite figure is made of a cylinder and a cone. Write each formula. Substitute known values. Find the value of the power. Multiply. Find the sum of the volumes. V ≈ 50. 24 + 12. 56 = 62. 8 The volume of the solid is about 62. 8 ft 3.

Find the approximate remaining volume when a cylindrical hole is drilled out of the prism. Use 3. 14 for . This prism is made of a prism and with a cylinder removed. Write the formulas needed. Substitute known values. Find the value of the power. Multiply. Find the difference of the volumes. V ≈ 512 – 100. 48 ≈ 411. 52 The remaining volume is about 411. 52 cm 3.

Exit Problem Find the volume of the composite solid. Use 3. 14 for .