Problem 1.10: Surfaces \( \rho=3 \) and \( \rho=5, \phi=100^{\circ} \) and \( 130^{\circ}, Z=3 \) and \( Z=4.5 \) define a chosed surface. Find: i Enclosed volume, ii. Total area of enclosed surface iii. Total length of Congest line that lies entirely within the volumbe. iv. Total length of all 12 edges. (S-22/23 for 7 marks)
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Enclosed volume: The volume of a cylindrical segment can be calculated using the formula V = hπ(r2^2 - r1^2), where h is the height of the cylinder, r2 is the outer radius, and r1 is the inner radius. In this case, h = 4.5 - 3 = 1.5, r2 = 5, and r1 = 3. So, the Show more…
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Figure $\mathrm{P} 1.14$ shows a frustrum of a cone. Of the following mensuration (geometrical) expressions, which describes (a) the total circumference of the flat circular faces (b) the volume (c) the area of the curved surface? (i) $\pi\left(r_{1}+r_{2}\right)\left[h^{2}+\left(r_{1}-r_{2}\right)^{2}\right]^{1 / 2}$ (ii) 2$\pi\left(r_{1}+r_{2}\right)$ (iii) $\pi h\left(r_{1}^{2}+r_{1} r_{2}+r_{2}^{2}\right)$
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