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3 years ago

Find radius of a hemisphere given volume of 144 cm³

Mathematics

1 answer:

marysya [2.9K]3 years ago

8 0

Answer:

The radius is 4.097396898

Step-by-step explanation:

A hemisphere is 1/2 of a sphere so the volume is 1/2 of the volume

V = 1/2 ( 4/3 pi r^3)

= 2/3 pi r^3

144 = 2/3 pi r^3

Multiply each side by 3/2

3/2 *144 = 3/2 * 2/3 pi r^3

216 = pi r^3

Divide each side by pi

216/ pi = pi r^3/pi

68.78980892 = r^3

Take the cube root of each side

(68.78980892 )^1/3= (r^3)^1/3

4.097396898 = r

The radius is 4.097396898

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11 halves divided by 7

Tamiku [17]

Answer:

$\large\boxed{\dfrac{11}{14}}$

Step-by-step explanation:

$\dfrac{\frac{11}{2}}{7}=\dfrac{11}{2}\div7=\dfrac{11}{2}\div\dfrac{7}{1}=\dfrac{11}{2}\cdot\dfrac{1}{7}=\dfrac{(11)(1)}{(2)(7)}=\dfrac{11}{14}$

4 0

3 years ago

Read 2 more answers

Write an inequality for the sentence: The total t is less than sixteen.

RoseWind [281]

T<16 is your inequality.

7 0

3 years ago

What is the value of r to the nearest tenth?

Tatiana [17]

Answer:

Hence r=10.3 cms (rounded to tenth place)

Step-by-step explanation:

In Triangle KLN ,

KN = 5 Cms

LN = ½ of LM

As the Perpendicular dropped from the center to the chord bisects it.

LM = 18 cm

LN = 9 cm

Now we have to find r or KL

We apply Hypotenuse Formula in this

The formula is given as

$c=\sqrt{a^2+b^2}$

Where c = r

a=5

b=9

Putting them in the formula

$r=\sqrt{5^2+9^2}$

$r=\sqrt{25+81}$

$r=\sqrt{106}$

$r=10.29$

5 0

3 years ago

In an office, there are 75 women and 125 men .Find the ratio of

schepotkina [342]

Given:

In an office, there are 75 women and 125 men.

To find:

The ratio of the number of men to the number of women.

Solution:

We have,

Number of men = 125

Number of women = 75

The ratio of the number of men to the number of women is:

$\text{Required Ratio}=\dfrac{\text{Number of men}}{\text{Number of women}}$

$\text{Required Ratio}=\dfrac{125}{75}$

$\text{Required Ratio}=\dfrac{5}{3}$

$\text{Required Ratio}=5:3$

Therefore, the ratio of the number of men to the number of women is 5:3.

4 0

2 years ago

A new school has x day students and y boarding students.

guapka [62]

Given:

The fees for a day student are $600 a term.

The fees for a boarding student are $1200 a term.

The school needs at least $720000 a term.

To show:

That the given information can be written as $x + 2y\geq 1200$ .

Solution:

Let x be the number of day students and y be the number of boarding students.

The fees for a day student are $\$600$ a term.

So, the fees for $x$ day students are $\$600x$ a term.

The fees for a boarding student are $\$1200$ a term.

The fees for $y$ boarding student are $\$1200y$ a term.

Total fees for $x$ day students and $y$ boarding student is:

$\text{Total fees}=600x+1200y$

The school needs at least $720000 a term. It means, total fees must be greater than or equal to $720000.

$600x+1200y\geq 720000$

$600(x+2y)\geq 720000$

Divide both sides by 600.

$\dfrac{600(x+2y)}{600}\geq \dfrac{720000}{600}$

$x+2y\geq 1200$

Hence proved.

3 0

3 years ago