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Lana71 [14]
3 years ago
12

A come and a pyramid has equal heights and volumes.if the base area of the pyramid is 154cm2.find the radius of the cone.

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
4 0

Answer:

Radius = 8.575 cm

Step-by-step explanation:

Formula for volume of a pyramid is;

V_p = ½Ah

Where A is area of base and h is height

Also, formula for volume of cone is given as;

V_c = ⅓πr²h

Now, we are told that V_p = V_c and that h is the same for both shapes.

Thus ;

½Ah = ⅓πr²h

h will cancel out to give;

½A = ⅓πr²

Cross multiply to give;

3A/2π = r²

Base area of pyramid is given as 154 cm². Thus;

(3 × 154)/2π = r²

r = √((3 × 154)/2π

r = 8.575 cm

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the brain volumes ​(​) of 50 brains vary from a low of to a high of . use the range rule of thumb to estimate the standard devia
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The estimated standard deviation from the range rule is 145.5 cm3.As it is 29.8 cm3 smaller than the exact standard deviation, we consider that the estimation is not accurate enough.

Generally, brain volumes which are smaller than 921.1 cm3 can be considered significantly low and bigger than 1417.5 cm3 can be considered significantly high. Hence, brain volume of 1457.5 cm3 is bigger than the expected maximum, so it can be considered significantly high.

The calculation goes like this,

According to the range rule, the standard deviation and range, or the distance between the maximum and smallest value, are roughly inversely proportional:

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If we have a sample of 50 brains volumes, and they range from 910 cm3 to 1492 cm3, we can estimate the standard deviation as:

s=max-min/4

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The exact standard deviation is 175.3 cm3.The difference is 175.3-145.5=29.8 cm3, so the estimation is not accurate enough.

The range rule of thumb states that we should anticipate a maximum value that is approximately two standard deviations above the mean and a lowest value that is approximately two standard deviations below the mean. The expected ranges are as follows given our mean volume of 1169.3 cm3 and standard deviation of 124.1 cm3:

Min= M-2s=1169.3-2*124.1=921.1

Max=M+2s=1169.3+2*124.1=1417.5

The brain capacity of 1457.5 cm3 can be regarded as significantly high because it is higher than the predicted maximum.

To know about standard deviation click here :

brainly.com/question/23907081

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2 years ago
Read 2 more answers
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(1073 + 1108 + x) / 3 = 1000
(2181 + x) / 3 = 1000 ....multiply both sides by 3
2181 + x = 1000 * 3
2181 + x = 3000
x = 3000 - 2181
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