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2 years ago

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The radius of the sphere is 10 units. What is the approximate volume of the sphere? Use and round to the nearest whole cubic uni

t. 42 cubic units 126 cubic units 4187 cubic units 73,385 cubic units

2 answers:

erica [24]2 years ago

4 0

Answer:

The approximate volume of the sphere= 4187 cubic units

Step-by-step explanation:

<u>Points to remember</u>

Volume of sphere = (4/3)πr³

Where 'r' radius of sphere

<u>To find the volume of sphere</u>

It is given that the radius of the sphere is 10 units. ,

Here radius r = 10 units

Volume = (4/3)πr³

= (4/3) * 3.14 * 10³

= (4/3) * 3140

= 4186.666 ≈ 4187 cubic units

VikaD [51]2 years ago

4 0

Answer:

Option C.

Step-by-step explanation:

Radius of the sphere is given as 10 units.

We have to calculate the volume of this sphere.

Since formula to measure the volume of sphere is V = $\frac{4}{3}\pi r^{3}$

V = $\frac{4}{3}\pi 10^{3}$

= $\frac{4}{3}(3.14)(10^{3})$

= 4186.67

≈ 4187 cubic units.

Option C. is the answer.

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Please answer all of them need this

VikaD [51]

First Question

For a better understanding of the solution provided here please find the first attached file which has the diagram of the the isosceles trapezoid.

We dropped perpendiculars from C and D to intersect AB at Q and P respectively.

As can be seen in $\Delta BCQ$ , we can easily find the values of CQ and BQ.

Since, $Sin(75^0)=\frac{CQ}{8}$

$\therefore CQ=8\times Sin(75^0)\approx 7.73$ ft

In a similar manner we can find BQ as:

$Cos(75^0)=\frac{BQ}{8}$

$BQ\approx2.07$ ft

All these values can be found in the diagram attached.

Thus, because of the inherent symmetry of the isosceles trapezoid, PQ can be found as:

$PQ=22-(AP+QB)=22-(2.07+2.07)=17.86$

Let us now consider $\Delta AQC$

We can apply the Pythagorean Theorem here to find the length of the diagonal AC which is the hypotenuse of $\Delta AQC$ .

$AC=\sqrt{(AQ)^2+(QC)^2}=\sqrt{(AP+PQ)^2+(QC)^2}=\sqrt{(2.07+17.86)^2+(7.73)^2}\approx21.38$ feet.

Thus, out of the given options, Option B is the closest and hence is the answer.

Second Question

For this question we can directly apply the formula for the area of a triangle using sines which is as:

Area= $\frac{1}{2}$ (First Side)(Second Side)(Sine of the angle between the two sides)

Thus, from the given data,

Area= $\frac{1}{2}\times 218.5\times 224.5\times sin(58.2^0)\approx20845$ $m^2$

Therefore, Option D is the correct option.

Third Question

For this question we will apply the Sine Rule to the $\Delta ABC$ given to us.

Thus, from the triangle we will have:

$\frac{AB}{Sin(\angle C)}=\frac{BC}{Sin(\angle A)}$

$\frac{c}{Sin(\angle C)}=\frac{a}{Sin(\angle A)}$

$\frac{17}{Sin(25^0)}=\frac{a}{Sin(45^0)}$

This gives $a$ to be:

$a\approx28.44$

Which is not close to any of the given options.

Fourth Question

Please find the second attachment for a better understanding of the solution provided her.

As can be clearly seen from the attached diagram, we can apply the Cosine Rule here to find the return distance of the plane which is CA.

$AC=\sqrt{(AB)^2+(BC)^2-2(AB)(BC)\times Cos(\angle B)}$

$\therefore AC=\sqrt{(172.20)^2+(111.64)^2-2(172.20)(111.64)\times Cos(177.29^0)}\approx283.8$ miles.

Thus, Option D is the answer.

8 0

2 years ago

Read 2 more answers

Last year Lenny had an annual earned income of $58,475. He also had passive income of $1,255, and capital gains of $2,350. What

Lelechka [254]

<u>Answer:</u> d. $62,080

<u>Step-by-step explanation:</u>

<u></u>

The capital gain is the profit earned from an investment whereas the passive income is the income generated by very minimal daily efforts.

Given: Annual income earned by Lenny = $\$58,475$

Passive income = $\$1,255$

Capital gain = $\$2,350$

Now, $\text{Total gross income =Annual income+Passive income+Capital gain}$

$=\$58,475+\$1,255+\$2,350=\$62,080$

Hence, Lenny's total gross income for the year = $62,080

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anzhelika [568]

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