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Finger [1]
3 years ago
7

Find the volume of a cone with base area 36π ft2 and a height equal to twice the radius. Give your answers both in terms of π an

d rounded to the nearest tenth.
The volume in terms of π is _____ft3.
The volume rounded to the nearest tenth is _____ft3.
Mathematics
1 answer:
Vikentia [17]3 years ago
7 0

Answer:

The volume in terms of π is 144 ft³

The volume rounded to the nearest tenth is 452.4 ft³

Step-by-step explanation:

The formula of the volume of a cone is V = \frac{1}{3} π r² h , where r is its radius and h is its height

The formula of the area of a circle is A = π r²

∵ The area of the base of the cone is 36π ft²

- Equate the formula of the area of the circle by 36π to find r

∵ πr² = 36π

- Divide both sides by π

∴ r² = 36

- Take √ to both sides

∴ r = 6 ft

∵ The height of the cone is equal to twice the radius

∵ The radius of the cone is 6 ft

- Multiply 6 by 2 to find the height

∴ h = 2(6) = 12 ft

∴ The height of the cone is 12 ft

Substitute the values of h and r in the formula of the volume of the cone to find it

∵ V = \frac{1}{3} π(6)²(12)

∴ V = 144 π ft³

∴ V = 452.3893421 ft³

- Round it to the nearest tenth

∴ V = 452.4 ft³

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2 years ago
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Using the t-distribution to build the 99% confidence interval, it is found that:

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  • The 99% confidence interval for the population mean is (19.36, 26.64).

<h3>What is a t-distribution confidence interval?</h3>

The confidence interval is:

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In which:

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The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 21 - 1 = 20 df, is t = 2.086.

The other parameters are given as follows:

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The margin of error is given by:

M = t\frac{s}{\sqrt{n}} = 2.086\frac{8}{\sqrt{21}} = 3.64

Hence the bounds of the interval are:

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The 99% confidence interval for the population mean is (19.36, 26.64).

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7 0
1 year ago
1/3x7 ...............
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3 years ago
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Answer:

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