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

Evaluate.

Radda [10]

Step-by-step explanation:

-| 12/3 - 1| 2-(-3)

-|12-3/3|5

-5|9/3|

-5|3|

-5×3 & -5×-3

-15 & 15

I think it is the answer

6 0

1 year ago

Multiply the polynomials show steps

Karo-lina-s [1.5K]

Answer:

3 $a^{4}$ + 11a³ - 7a² + 18a - 18

Step-by-step explanation:

When multiplying with two brackets, you need to multiply the three terms, (a²), (4a) and (-6) from the first bracket to all the terms in the second brackets, (3a²), (-a) and (3) individually. I have put each multiplied term in a bracket so it is easier.

(a² + 4a - 6) × (3a² - a + 3) =

(a² × 3a²) + {a² × (-a)} + (a² × 3) + (4a × 3a²) + {4a × (-a)} + (4a × 3) + {(-6) × a²) + {(-6) × (-a)} + {(-6) × 3}

Now we can evaluate the terms in the brackets.

(a² × 3a²) + {a² × (-a)} + (a² × 3) + (4a × 3a²) + {4a × (-a)} + (4a × 3) + {(-6) × a²) + {(-6) × (-a)} + {(-6) × 3} =

3 $a^{4}$ + (-a³) + 3a² + 12a³ + (-4a²) + 12a + (-6a²) + 6a + (-18)

We can open the brackets now. One plus and one minus makes a minus.

3 $a^{4}$ + (-a³) + 3a² + 12a³ + (-4a²) + 12a + (-6a²) + 6a + (-18) =

3 $a^{4}$ -a³ + 3a² + 12a³ -4a² + 12a -6a² + 6a -18

Evaluate like terms.

3 $a^{4}$ -a³ + 3a² + 12a³ -4a² + 12a -6a² + 6a -18 = 3 $a^{4}$ + 11a³ - 7a² + 18a - 18

5 0

3 years ago