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BabaBlast [244]
2 years ago
7

A right prism has a volume of 65 cubic inches. The prism is enlarged so its height is increased by a factor of 20, but the other

dimensions do not change. What is the new volume? A.1000 in .3 B.1300 in .3 C.1200 in. 3 D. 1100 in.3
Mathematics
1 answer:
Helga [31]2 years ago
8 0

Answer:

Volume of a right prism = 65 cubic inches

Its height is increased by a factor of 20.

To find:

The new volume of the prism if the other dimensions do not change.

Solution:

The volume of a prism is:

Volume=Bh

Where, B is the base area and h is the height.

A right prism has a volume of 65 cubic inches.

65=Bh

The height of prism is increased by a factor of 20. So, the new volume is:

Volume=B(20h)

Volume=20(Bh)

Volume=20(65)

Volume=1300

The volume of the new prism is 1300 in³.

Therefore, the correct option is B.

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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving
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Answer:

The volume of the solid is 714.887 units³

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* Lets solve the problem

∵ y = x^{\frac{5}{2}}

∵ The plane region is revolving about the y-axis

∵ y = 32 and x = 0

- Lets find the volume by the shell method

- The definite integral are x = 0 and the value of x when y = 32

- Lets find the value of x when y = 0

∵ y = x^{\frac{5}{2}}

∵ y = 32

∴ 32=x^{\frac{5}{2}}

- We will use this rule to find x, if x^{\frac{a}{b}}=c, then=== x=c^{\frac{b}{a}} , where c

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∴ x=(32)^{\frac{2}{5}}=4

∴ The definite integral are x = 0 , x = 4

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∵ V = \int\limits^a_b {2\pi}xf(x) \, dx

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∴ V=2\pi \int\limits^4_0 {x}.x^{\frac{5}{2}}\, dx

- simplify x(x^5/2) by adding their power

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- The rule of integration of x^{n} is ==== \frac{x^{n+1}}{(n+1)}

∴ V = 2\pi \int\limits^4_0 {x^{\frac{9}{2}}} \, dx=2\pi[\frac{x^{\frac{9}{2}}}{\frac{9}{2}}] from x = 0 to x = 4

∴ V=2\pi[\frac{2}{9}x^{\frac{9}{2}}] from x = 0 to x = 4

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∴ V=2\pi[\frac{2}{9}(4)^{\frac{9}{2}}-\frac{2}{9}(0)^{\frac{9}{2}}}]=2\pi[\frac{1024}{9}-0]

∴ V=\frac{2048}{9}\pi=714.887

* The volume of the solid is 714.887 units³

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