In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ar3 and its curved surface area is given by 2ar2. (a) 2 h cm r cm Figure 3 Figure 3 shows a solid which is made up of a cylinder with radius r cm and height h cm. A hemisphere of radius r cm is attached to one end of the cylinder. The total surface area of the solid is 2000n cm?. i. Express h in terms of r. ii. Show that the volume of the solid, V, is given by V = 1000ar – ar³ . 5 ii. Use calculus to find the value of r which gives the maximum volume. iv. Confirm that your value of r gives a maximum.

In this question, you may find the following helpful. For a hemisphere of radius r, its volume is given by ar3 and its curved surface area is given by 2ar2. (a) 2 h cm r cm Figure 3 Figure 3 shows a solid which is made up of a cylinder with radius r cm and height h cm. A hemisphere of radius r cm is attached to one end of the cylinder. The total surface area of the solid is 2000n cm?. i. Express h in terms of r. ii. Show that the volume of the solid, V, is given by V = 1000ar – ar³ . 5 ii. Use calculus to find the value of r which gives the maximum volume. iv. Confirm that your value of r gives a maximum.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.

Question

i just need (iv) and (B)

The last two questions

Question B5
In this question, you may find the following helpful.
For a hemisphere of radius r, its volume is given by ar3
and its curved surface area is given by 2nr?.
(а)
2
h cm
r cm
Figure 3
Figure 3 shows a solid which is made up of a cylinder with radius r cm
and height h cm. A hemisphere of radius r cm is attached to one end of
the cylinder.
The total surface area of the solid is 2000n cm?.
i.
Express h in terms of r.
ii.
5
Show that the volume of the solid, V, is given by V = 1000r
iii. Use calculus to find the value of r which gives the maximum volume.
iv. Confirm that your value of r gives a maximum.
(b) Use calculus to explain why the curve with equation y = lIn x has a positive
gradient for all values of x.

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