Calculate volumes, 𝑉, and capacities of standard three-dimensional objects in practical situations, including rectangular prisms, cylinders, pyramids, cones, spheres and composites.  prism: 𝑉 = 𝐴ℎ where 𝐴 is base area and ℎ is perpendicular height  cylinder: 𝑉 = 𝜋𝑟2 ℎ where 𝑟 is radius and ℎ is perpendicular height  pyramid: 𝑉 = 1 3 𝐴ℎ where 𝐴 is base area and ℎ is perpendicular height  cone: 𝑉 = 1 3 𝜋𝑟2 ℎ where 𝑟 is radius and ℎ is perpendicular height  sphere: 𝑉 = 4 3 𝜋𝑟3 where 𝑟 is radius

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Question 1

A grain silo consists of a cylindrical body with a conical roof and a conical hopper base. The table shows the dimensions for three different silo designs. A farmer needs to store 480 cubic metres of wheat and wants to choose the silo design with the smallest total external surface area to minimise painting costs. Calculate the total volume and the total external surface area of each silo design to determine which design the farmer should choose.

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