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3 years ago

If the volume of a full sphere is 4/3 x pi x radius cubed, what is the volume of a half sphere, also called a hemisphere?

Mathematics

2 answers:

Varvara68 [4.7K]3 years ago

8 0

Answer:

Volume of Hemisphere = $\frac{2}{3} \pi r^{3}$

Step-by-step explanation:

Half of a full sphere is called a Hemisphere.

Volume of Hemisphere is half of that of a sphere.

Volume of sphere = $\frac{4}{3} \pi r^{3}$

Volume of Hemisphere = $\frac{4}{3}\pi r^{3}$ ÷ 2

Or Volume of Hemisphere = $\frac{2}{3} \pi r^{3}$

Lady bird [3.3K]3 years ago

7 0

The formula for a hemisphere is: 2/3 π r

if there was a problem to solve, i would be happy to do it.

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You are looking at a 260 foot by 180 foot building lot to subdivide and build two houses. Your town requires 1/2 acre (one acre

Varvara68 [4.7K]

Answer:

You have 1.07 acres in this building lot and you can only build 2 houses.

Step-by-step explanation:

You are looking at a 260 foot by 180 foot building lot to subdivide and build two houses.

We are given that 1 acre = 43,560 square feet.

In this building plot (260 foot by 180 foot), the area is:

260 * 180 = 46,800 square feet

Hence, the number of acres we have in this lot is:

$\frac{46800}{43560} = 1.07$

Since your town requires 1/2 acre to build a house, the number of houses that you can build on it will be:

$\frac{1.07}{\frac{1}{2} } = 1.07 * 2 = 2.14$

Since the number of houses can only be whole number, we approximate to nearest whole number ≅ 2 houses.

You have 1.07 acres in this building lot and you can only build 2 houses.

4 0

3 years ago

Solve the following:

Yuliya22 [10]

Answer:

-4

Step-by-step explanation:

9^2+19/(10^2-5^3)

9^2+19/(10^2-5^3)=81+19/100-125

9^2+19/(10^2-5^3)=81+19/100-125=100/-25

9^2+19/(10^2-5^3)=81+19/100-125=100/-25= -4

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2 years ago

The hospital is 3.1 miles west of the fire station. What is the length of straight line between the school and the hospital? Rou

kenny6666 [7]

Answer:

2.1 miles

Step-by-step explanation:

5 0

3 years ago

One strange phenomenon that sometimes occurs at U.S. airport security gates is that an otherwise law-abiding passenger is caught

valentinak56 [21]

Answer:

c. 0.16

Step-by-step explanation:

For each passenger there are only two possible outcomes. Either they are caught with a gun, or they are not. The probability of a passenger being caught with a gun is independent from other passengers. So we use the binomial probability distribution to solve this question.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .