6 mm

A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t

Vlad1618 [11]

Answer:

$185553.7\text{ feet}^3$

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

5 0

3 years ago

What is the equation of the line that passes through 1,4 and 2,1

sashaice [31]

Answer:

y = -3x + 7

Step-by-step explanation:

The equation of a line

y = mx + c

y - intercept point y

m - slope of the line

x - intercept point x

c - intercept point of the line

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given two points

( 1 , 4) ( 2 , 1)

x1 = 1

y1 = 4

x2 = 2

y2 = 1

insert the values

m = 1 - 4 / 2 - 1

m = -3/1

m = -3

y = -3x + c

Step 2: substitute any of the two points given into the equation of a line

y = -3x + c

( 1 ,4)

x = 1

y = 4

4 = -3(1) + c

4 = -3 + c

4 + 3 = c

c = 7

Step 3: sub c into the equation

y = -3x + 7

The equation of the line is

y = -3x + 7

3 0

3 years ago

Jeremy unpacked 18

tekilochka [14]

Answer:

40

Step-by-step explanation: 40 x .45 = 18

7 0

3 years ago

What is the common ratio of 40,12,3.6

slava [35]

Answer:

0.3

Step-by-step explanation:

Divide the second term (12) with the first term (40), and you'll get 0.3

This is correct because you get the terms in the correct order when multiplying:
(First term: 40. Common ratio: 0.3)
40 x 0.3 = 12
12 x 0.3 = 3.6

40, 12, 3.6

3 0

2 years ago

Hurry!!!Between which two values would 75% of the data represented on a box plot lie? Check all that apply.

sp2606 [1]

the answers are the lower quartile and the maximum and The minimum and the upper quartile.

4 0

3 years ago

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