All categories

2 years ago

A sphere has a surface area of about 999 square millimeters. What is the radius, in millimeters, of the sphere

Mathematics

1 answer:

motikmotik2 years ago

5 0

Given that, a sphere has a surface area of about 999 square millimeters.

Formula to find the surface area of sphere is,

S= 4πr² Where r = radius of the sphere and S= surface area.

Given S= 999 square millimeters.

So, we can write:

4πr² = 999

4 * 3.14 * r² = 999 Since, π = 3.14

12.56 *r² = 999

$r^2=\frac{999}{12.56}$ Divide each sides by 12.56.

r² = 79.53821656

r = √79.53821656 Taking square root to each sides of equation.

r = 8.918420071

So, r = 8.918 Rounded to nearest thousandth.

So, radius of the sphere is 8.918 millimeters.

Hope this helps you!

You might be interested in

COOKING Franklin is cooking a 3-pound turkey breast for 6 people. If the number of pounds of turkey varies directly with the num

Gwar [14]

<u>Answer-</u>

2, 4, and 8 people will need 1, 2, 4 pounds of turkey respectively.

<u>Solution-</u>

Given in the question, number of pounds of turkey varies directly with the number of people, i.e as the number of people increases or decreases, the pound of turkey also increases or decreases.

Taking,

x = number of people,

y = pounds of turkey.

This condition can be represented as,

$\Rightarrow y\ \alpha \ x\\\Rightarrow y=kx$

As given in the question, when x = 6 y = 3

$\Rightarrow 3=k\times 6$

$\Rightarrow k=\frac{3}{6}= \frac{1}{2}$

Now, putting the values of k in the equation, the equation becomes

$\Rightarrow y=\frac{1}{2}x$

Now, we can get the values of y or number of pounds of turkey needed by putting the given x or number of people.

All the calculations are shown in the attached table.

5 0

2 years ago

the first term of an arithmetic sequence is 2 and the sum of the first 15 terms is 292.5. Find the common difference

adelina 88 [10]

Given:

First term of an arithmetic sequence is 2.

Sum of first 15 terms = 292.5

To find:

The common difference.

Solution:

We have,

First term: $a=2$

Sum of first 15 terms: $S_{15}=292.5$

The formula of sum of first n terms of an AP is

$S_n=\dfrac{n}{2}[2a+(n-1)d]$

Where, a is first term and d is common difference.

Putting $S_{15}=292.5$ , n=15 and a=2 in the above formula, we get

$292.5=\dfrac{15}{2}[2(2)+(15-1)d]$

$292.5=\dfrac{15}{2}[4+14d]$

$292.5=15[2+7d]$

Divide both sides by 15.

$\dfrac{292.5}{15}=2+7d$

$19.5=2+7d$

$19.5-2=7d$

$17.5=7d$

Dividing both sides by 7, we get

$\dfrac{17.5}{7}=d$

$2.5=d$

Therefore, the common difference is 2.5.

8 0

2 years ago

SOLVE for me. All multiple choice

tester [92]

9: B right

10: C obtuse

11: B right

12: B right

I hope they are right! Sorry if they are not!

6 0

2 years ago

In the accompanying diagram of right triangle ABC, the hypotenuse if AB, AC = 3, BC = 4, and AB = 5. Sin B is equal to

Trava [24]

Answer: $sin(B)=\frac{3}{5}$

Step-by-step explanation:

We are given that a triangle ABC is a Right Angled Triangle. The side AB is hypotenuse, so the angle opposite to side AB which will be angle C is a Right Angle (measures 90 degrees)

We have the side length of all 3 sides. Based on this information, we can construct a triangle with given measures. The triangle is shown in the attached image.

We have to find the value of Sin(B). Sin of an angle is defined as:

$sin(\theta)=\frac{\text{Opposite Side}}{\text{Hypotenuse}}$

The side opposite to angle B is AC with a length of 3 and hypotenuse is side AB with length 5. So Sin of angle B would be:

$sin(B)=\frac{3}{5}$

8 0

2 years ago

Which is the longest? 100mm, 5cm,1/2m

GenaCL600 [577]

Answer:100mm

Step-by-step explanation:

7 0

2 years ago