Question: In this problem we will use the line segment PQ, where P= (1,3) and Q = (3,7). (a) Find the length of the line

In this problem we will use the line segment PQ, where P= (1,3) and Q = (3,7). (a) Find the length of the line segment PQ using (i) the distance formula. (ii) integration with respect to z. (iii) integration with respect to y. (b) Create a frustum of a cone by rotating the line segment PQ about the z-axis. Find the surface area of the resulting frustum of a cone by using (i) the surface area formula for a frustrum of a cone. (ii) integration with respect to z. (iii) integration with respect to y. (c) We now create a frustum of a cone by rotating the line segement PQ about the line y=-1. Find the area of the resulting frustum using (i) the surface area formula for a frustrum of a cone. Explain what changes compared to (b)(i) and what stays the same. (ii) integration with respect to r. (iii) integration with respect to y. (Hint: draw the frustum and find its dimensions.)

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