7. A capsule in the form of a cylinder of length t cm with hemisphere of radius r cmis shown in Figure 1. The surface area of the capsule is 2 cm².OFigure 1i)ii)Find the maximum volume of the capsule.Show that the volume of the capsule is V=r-Find the value(s) of r so that the volume of the capsule is maximum.two ends

A capsule in the form of a cylinder of length t cm with a hemisphere of radius r сm at two ends is…

Answered: 7. A capsule in the form of a cylinder…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A vertical dam has the form of an isosceles trapezoid with horizontal sides parallel. The dam is 20 m high, 20 m in its lower part and 40 m in its upper part. Finally, the dam retains 15 m of water, as indicated in the figure below. 20 - 20 15 a) Let y denote the height in meters measured from the base of the dam. The hydrostatic force exerted by the water on the portion of the dam comprised between y m and y + Ay m is approximately p (y) Ay N. What is p (y)? Note that the density of water is p = 1000 Kg/m³ and the acceleration due to gravity on the earth's surface is g = 9.8 m/s2 Express your answer as a formula Answer: b) in Newtons, what is the total hydrostatic force exerted on the dam? FORMATTING: If you round your answer, ensure that the round-off error is less than 1% of the value. Answer Number
Let "r" and "h" be the radius and height, respectively, of the right circular cylinder of maximum volume that can be inscribed in a right circular cone of radius R = 18 and height H = 9. Determine the value of "r" + "h". (image in portuguese if you have doubts about the measurements)
6) Line y=xbetween x = 0 and x = 1 is rotating around the x - axis. (It forms a cone). Calculate a) The volume of the resulting cone b) The surface area of the cone
a) How much less is the volume of the cone than b) Using R = the volume of the cylinder of the same height? find the volume of the hemisphere, correct to 2 decimal places. (Use n = - 꼭) 7 cm 7 m - 21 cm Tr2h V1 of a cylinder = Tr’h, V2 of a cone V = Tr2h V,– V½ = rr’h - 3 2nr2h 3 11 =2x Simplify m² = 11 x 7x7 cm c) Using t = 3.14 find the volume of the shape. d) Using n= find the volume of the shaded 7 00 space. -14 cm mm -10 mm - V = V = mm3 cm II -6 cm- II 3.
7. A capsule in the form of a cylinder of length t cm with hemisphere of radius r cm at two ends is shown in Figure 1. The surface area of the capsule is 2 cm². i) Figure 1 Show that the volume of the capsule is V=r- m³. Find the value(s) of r so that the volume of the capsule is maximum. Find the maximum volume of the capsule.
Slove the math step by step.Also mention the graph.Don't give short answer And don't give math in text from that i don't understand.

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