The figure shows a frustrum of a cone. Match each ...

Question

The figure shows a frustrum of a cone. Match each of the expressions (a) π(r₁ + r₂)[h² + (r₂ − r₁)²]^1/2 (b) 2π(r₁ + r₂) and (c) πh(r₁² + r₁r₂ + r₂²)/3 with the quantity it describes: (1) the total circumference of the flat circular faces (2) the volume or (3) the area of the curved surface

Patrick Ford · Accepted Answer

In this problem, we'll verify the correct expression against the proper dimension of the quantity described.We'll assume the lengths are in meters.Circumference dimension: L (m)[readmore]Volume dimension: L3 (m3)Area dimension: L2 (m2)We'll assume that r1 = r2 = h = L (a) π(r1 + r2)[h2 + (r2 − r1)2]1/2 = π(L + L)[L2 + (L - L)2)(1/2) = π(2L)(L(2/2)) = 2πL2 (m2)(b) 2π(r1 + r2) = 2π(L + L) = 4πL (m)(c) πh(r12 + r1r2 + r22)/3 = πL(L2 + L•L + L2)/3 = πL(3L2)/3 = πL3 (m3)(1)The circumfrrnce is a length. It is proper dimension is m.The expression with the dimension of a length is (b) 2π(r1 + r2)The correct expression for the total circumference of the flat circular faces is (b) 2π(r1 + r2)(2)The proper dimension of the volume is m3.The expression with the dimension of a volume is (c) πh(r12 + r1r2 + r22)/3The correct expression for the volume is (c) πh(r12 + r1r2 + r22)/3(3)The proper dimension of an area is m2.The expression with the dimension of a length is  (a) π(r1 + r2)[h2 + (r2 − r1)2]1/2 The correct expression for the area of the curved surface is  (a) π(r1 + r2)[h2 + (r2 − r1)2]1/2

FREE Expert Solution

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FREE Expert Solution

Problem Details

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