3 (width), H (height). It is hollowed by a cylinder with dimensions R (base radius) and (height). The dimensions at any instant (t) are: == √e² - t², B = t³ + 7/²/2 H = 2cosht 3 R = t + Int The volume of the box is (Vbox = LBH) and the volume of cylinder is (Vcylinder = лR²H). dv Find the rate of change of the volume () for this body at t = 2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Q2: The body shown in figure is a rectangular box whose dimensions are L (length),
B (width), H (height). It is hollowed by a cylinder with dimensions R (base radius) and
H (height).
The dimensions at any instant (t) are:
ti
L = √et-t² B = t³ + ²/²/2
= 2cosht
"
3
R = t + Int
The volume of the box is (Vbox = LBH) and the volume of cylinder is (Vcylinder = TR²H).
Find the rate of change of the volume for this body at t = 2.
dt
Transcribed Image Text:Q2: The body shown in figure is a rectangular box whose dimensions are L (length), B (width), H (height). It is hollowed by a cylinder with dimensions R (base radius) and H (height). The dimensions at any instant (t) are: ti L = √et-t² B = t³ + ²/²/2 = 2cosht " 3 R = t + Int The volume of the box is (Vbox = LBH) and the volume of cylinder is (Vcylinder = TR²H). Find the rate of change of the volume for this body at t = 2. dt
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