PLEASE HELP ME! i have this homework due tomorrow and i only have 1 question left and am sooo desperate for an answer:

The diameter of the Dome of the Rock in Jerusalem is 20m. If it is plated with gold that is 5cm thick, find the cost of plating the dome in gold given that 1kg of gold costs $43,395 and 1g of gold is equal to 19.3cm>3

p.s cm>3 means cm cube

surface area of sphere = (4/3) pi r^2

so
surface area of hemisphere = (2/3)pi r^2
here r = 10 m
so
surface area = (200/3) pi meters^2
there are 10^4 cm^2 per meter^2
so
surface area = (200/3) pi*10^4 cm^2
volume = surface area * depth
= (200/3) pi *10^4 * 5 cm^3
grams = volume*density
= (200/3) pi *10^4 * 5 (1/19.3)
cost per gram = 43.395
so
cost = (200/3) pi *10^4 * 5 (1/19.3)*43.395

The volume of the gold would be

V = (pi/4)D^2*(thickness) = 15.7 m^3
= 15.7*10^6 cm^3

The mass would be (density)*V = 303.2 *10^6 g = 303.2*10^3 kg

Multiply that by the cost per kg.

I get about 13 billion dollars

I treated it as a 5 cm layer over a cylinder. Damon treated it as a hemisphere. He is correct.

http://www.historyofscience.com/G2I/timeline/images/dome_of_the_rock.jpg

thank you sooo much damon :)

Sure, I can help you with that! To find the cost of plating the dome in gold, we need to calculate the volume of gold required and then multiply it by the cost per kilogram.

First, let's calculate the volume of gold required to plate the dome. Since the dome is in the shape of a semi-sphere, we can use the formula for the volume of a sphere:

V = (4/3) * π * r^3

Given that the diameter of the dome is 20m, the radius (r) would be half of that, which is 10m. Now let's convert the radius from meters (m) to centimeters (cm) since the thickness of the gold is given in centimeters:

10m = 10,000cm

Substituting the radius into the volume formula, we have:

V = (4/3) * π * (10,000)^3 cm^3

Next, we need to subtract the volume of the hollow part of the dome from the total volume. The thickness of the gold plating is 5cm, so we need to subtract the volume of the inner semi-sphere with a radius of 9.95m (since the thickness is 5cm, the radius is reduced by 5cm):

V_inner = (4/3) * π * (9,950)^3 cm^3

Finally, we can calculate the volume of gold required:

V_gold = V - V_inner

Now that we have the volume of gold required, we can convert it into kilograms using the conversion factor given in the question (1g of gold = 19.3cm^3):

V_gold_kg = V_gold / (19.3cm^3/g) / 1000kg/g

To find the total cost of plating the dome, we multiply the volume of gold in kilograms by the cost per kilogram, which is $43,395:

Cost = V_gold_kg * $43,395

By plugging in the calculated values into the equations above, you should be able to find the answer to your question.