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3 years ago

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25. If the scale factor of two similar solids is 3:16, what is the ratio of their corresponding areas and volumes? (1 point) 3:2

56 and 3:4,096 27:4,096 and 9:256 6:32 and 9:48 9:256 and 27:4,096 26. The volumes of two similar solids are 1,331 m3 and 216 m3. The surface area of the larger solid is 484 m2. What is the surface area of the smaller solid? (1 point) 864 m2 288 m2 144 m2 68 m2

2 answers:

kicyunya [14]3 years ago

8 0

Answer:

Question 25. Ratio of areas = $\frac{9}{256}$ and ratio of volumes = $\frac{27}{4096}$

Question 26. Surface area of smaller solid is 144 m²

Step-by-step explanation:

Question 25. The scale factor of two similar solids is 3 : 16.

We have to find out the ratio of their corresponding areas and volumes.

Since area is two dimensional unit, means area can be represented as multiplication of two dimensions.

If their sides are in the ratio of 3 : 16 then the ratio of their area will be = $\frac{3^{2} }{16^{2}}=\frac{9}{256}$

Similarly volume is three dimensional means it represents multiplication of three dimensions.

So the ratio of their volumes = $\frac{3^{3} }{16^{3} }=\frac{27}{4096}$

Question 26. Volume of two similar solids are 1331 m³ and 216 m³

Surface area of the larger solid is 484 m² then we have to find the surface area of the smaller solid.

As we have done in question number 25, ratio of dimensions of two solids will be = $\sqrt[3]{\frac{1331}{216}}=\frac{11}{6}$

Since we have calculated the ratio of dimensions of two solids so ratio of their area will be = $\frac{11^{2} }{6^{2}}=\frac{121}{36}$

Now we will use this ratio to determine the value of surface area of the smaller solid.

$\frac{121}{36}=\frac{484}{x}$

By cross multiplication

(121).x = (36).(484)

$x=\frac{(36).(484)}{121}$

x = 36×4 = 144 m²

Option C. is correct.

vitfil [10]3 years ago

3 0

I'm not sure about #25 but #26 is C. 144

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Answer:

a

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The alternative hypothesis is $H_a : \mu \ne 13.4000$

The null hypothesis is rejected

b

The 99% confidence level is $13.3930 < \mu < 13.3994$

Step-by-step explanation:

From the question we are told that

The sample size is n = 10

The population mean is $\mu = 13.4 000 \ angstroms$

The level of significance is $\alpha = 0.05$

The sample data is

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

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=> $\= x = 13.3962$

Generally the sample standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum (x_i - \= x)^2}{n} }$

=> $\sigma = \sqrt{\frac{ (13.3987 - 13.3962)^2 + (13.3987 - 13.3962)^2 + \cdots + (13.3987 -13.4002)^2 }{10} }$

=> $\sigma =0.0039$

The null hypothesis is $H_o : \mu = 13.4000$

The alternative hypothesis is $H_a : \mu \ne 13.4000$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu}{\frac{\sigma}{\sqrt{n} } }$

=> $z = \frac{13.3962 - 13.4000}{\frac{0.0039}{\sqrt{10} } }$

=> $z = 3.08$

Generally the p-value is mathematically represented as

$p-value = 2P( z > 3.08)$

From the z-table $P(z > 3.08)= 0.001035$

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$p-value = 2* 0.001035$

$p-value = 0.00207$

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$p-value < \alpha$

Hence the null hypothesis is rejected

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$\alpha = (100 -99)\%$

=> $\alpha = 0.01$

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$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 2.58 * \frac{0.0039}{\sqrt{10} }$

=> $E = 0.00318$

Generally the 99% confidence interval is mathematically represented as

$13.3962 - 0.00318 < \mu < 13.3962 + 0.00318$

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Answer:

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