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3 years ago

8

A giant pencil, in the shape of a cylinder, has a length of 36 inches and a diameter of 6 inches. On top, it has a cone-shaped t

ip with a height of 4 inches. What is the volume of the pencil terms of pi?

1 answer:

zysi [14]3 years ago

4 0

R=3
Vcyl.=36(9π)=324π
Vcone=4(9π)=36π
V pencil=324π+36π=360π

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konstantin123 [22]

Answer:

1. 10 square yards

2. $9.10

3. 36 girls

4. 20 cherries

5. 159 bracelets

Step-by-step explanation:

1.

The area of this figure would be the area of the SQUARE minus the area of the RECTANGLE (taken out).

The middle part is taken out (this is a rectangle).

View this as a square with sides 4 by 4 with a rectangle portion taken out. So the area can be said as:

Area = Area of Whole Square - Area of Middle Rectangle Taken Out

Lets calculate:

Area of Whole Square:

side * side = 4 * 4 = 16

Now,

Area of Middle Rectangle Taken Out:

Length * Width

The length is given as 3

The width would be 4 - two 1 from two sides, that is 4 - 1 - 1 = 2

So, area = 3 * 2 = 6

Area of figure = 16 - 6 = 10 square yards

2.

We have to find 20% of the bill.

The bill was 45.50 and we have to find 20% of 45.50.

We first convert percentage to decimal by dividing by 100:

20% = 20/100 = 0.20

Now we multiply this decimal with the bill to get our desired answer:

0.20 * 45.50 = $9.10

The tip is $9.10

3.

The ratio of boys (b) to girls (g) would be 2 is to 3.

There are 24 boys.

We can set up a ratio (fraction) with boys on top and girls on bottom.

Then we equate it with actual number of boys and girls (let it be g). So the ratio set-up would be:

$\frac{2}{3}=\frac{24}{g}$

To solve for g, the number of girls, we have to cross multiply and use algebra to solve. The process is shown below:

$\frac{2}{3}=\frac{24}{g}\\2*g = 24*3\\2g=72\\g=\frac{72}{2}\\g=36$

There are 36 girls in sixth grade

4.

For every "9" lemon, there are "4" cherries.

There are 45 lemons

If we think of "9" lemons as a "box", how many boxes of lemons are there?

45/9 = 5

Similarly, there would be "5" boxes of cherries. But there are "4" cherries per box. So there are:

4 * 5 = 20 cherries

We can also set up a ratio of cherry to lemon as 4 is to 9 and equate it with actual cherries (let it be "c") and lemons (45). Cross multiply and use algebra to solve for cherries ("c"). Algebra process shown below:

$\frac{Cherries}{Lemons}=\frac{4}{9}=\frac{c}{45}\\9*c=4*45\\9c=180\\c=\frac{180}{9}\\c=20$

See, we have the same answer, 20 cherries!

5.

Number sold total = 14 + 27 + 45 = 86

She still has 73 in her stock

So, she basically started with whatever she now has (73) and whatever she has sold the 3 days (86), that would be:

73 + 86 = 159 bracelets

Tia started with 159 bracelets

4 0

3 years ago

57 students choose to attend one of three after school activities: football, tennis or running.

skelet666 [1.2K]

The probability that the randomly selected student chose running is; 12/57

<h3>Solving Probability Questions</h3>

Total number of students = 57

Total number of boys = 24

Total number of girls = 33

Number of Girls that chose football = 17

Number of boys that chose football = 14

Number of students that chose Tennis = 14

Now, number of students that chose running will be;

Number of students that chose running = 57 - (31 + 14) = 12

Thus, probability that a randomly selected student chose running = 12/57

Read more about probability selection at; brainly.com/question/251701

3 0

2 years ago

At the dog park, 2 dogs are black with spots, 5 dogs are white with spots, 1 dog is solid white, and 4 dogs are solid black. Wha

Nikolay [14]

Its 11/12 , you need to divide the "wanted results" (every dog which is either black, with spots or both ) by every every possible result ( all dogs ). so 11/12=0.92

5 0

3 years ago

Read 2 more answers

0.35 in expanded form

Diano4ka-milaya [45]

Answer:0.3+0.05

Step-by-step explanation:

7 0

3 years ago

From A to B a private plane flies 2.8 hours at 110 mph on a bearing of 64 degrees . It turns at point B and continues another 1.

Firdavs [7]

Answer:

a. 360.323 m

b. $95.265^{o}$

Step-by-step explanation:

Distance covered from A to B = speed x time

= 110 x 2.8

= 308 m

Distance covered from B to C = speed x time

= 110 x 1.7

= 187 m

The sum of angles at B = $64^{o}$ + $26^{o}$

= $90^{o}$

a. The distance of the plane from it starting point to C can be determined by applying the cosine rule.

$b^{2}$ = $a^{2}$ + $c^{2}$ - 2ac Cos B

Sot hat;

$b^{2}$ = $187^{2}$ + $308^{2}$ - 2(187 x 308) Cos $90^{o}$

But, Cos $90^{o}$ = 0

So that,

$b^{2}$ = $187^{2}$ + $308^{2}$

= 34969 + 94864

= 129833

b = $\sqrt{129833}$

= 360.323

The distance from A to C is 360.323 m.

b. Applying the sine rule;

$\frac{a}{SinA}$ = $\frac{b}{SinB}$

$\frac{187}{SinA}$ = $\frac{360.323}{Sin90^{o} }$

$\frac{187}{SinA}$ = $\frac{360.323}{1}$

Sin A = $\frac{187}{360.323}$

= 0.5190

⇒ A = $Sin^{-1}$ 0.5190

= $31.265^{o}$

The bearing of the plane from its original location = $64^{o}$ + $31.265^{o}$

= $95.265^{o}$

8 0

3 years ago