Answer:
The volume of the sphere is 
Step-by-step explanation:
we know that
The volume of cylinder is equal to
we have
substitute
simplify
Remember that
A sphere and a cylinder have the same radius and height
so
The height of cylinder is equal to the diameter of sphere
h=2r
substitute
-----> equation A
The volume of the sphere is equal to
substitute equation A in the formula of the volume of sphere
1. The information given in the problem is:
- <span>The length of a rectangular garden is 8 feet longer than the width.
- </span><span>The garden is surrounded by a 4-foot sidewalk.
- The area of the sidewalk is 320 ft</span>².
2. So, the length of the rectangular garden is:
L1=8+W1
3. The formula for calculate the area of the sidewalk, is:
A2=L2xW2
"A2" is the area of the sidewalk (A2=320 ft²).
"L2" is the length of the sidewalk.
"W2" is the widht of the sidewalk.
4. The length of the sidewalk (L2) is:
L2=L1+4+4 (4 feet on each side)
L2=L1+8
5. When you substitute L1=8+W1 into the equation L2=L1+8, you obtain:
L2=8+W1+8
L2=W1+16
6. The widht of the sidewalk is:
W2=W1+4+4
W2=W1+8
7. Now, you must substitute the length and the widht of the sidewalk into the formula A2=L2xW2:
A2=L2xW2
A2=(W1+16)(W1+8)
320=W1²+16W1+8W1+128
W1²+16W1+8W1+128-320=0
W1²+16W1+8W1-192=0
8. When you solve the quadratic equation, you obtain the value of W1:
W1=16.97 ft
9. Finally, you must substitute the value of W1 into the formula L1=8+W1:
L1=8+W1
L1=8+16.97
L1=24.97 ft
10. Therefore, the dimensions of the garden are:
L1=24.97 ft
W1=16.97 ft
A = bh
A = 67 x 52
A = 3484
answer
B. 3484 ft^2
We are told in the question that 1 carat is equal to 200 mg.
The Hope Diamond is 44.5 carats. Let's multiply the weight of 1 carat by 44.5 to get the weight of the Hope Diamond in mg:
The total weight of the Hope Diamond is 8,900 mg. However the question asks for the weight in grams. There are 1000 mg in 1 gram, so let's divide the known weight of the Hope Diamond in mg by 1000 to get the weight converted to grams:
Now we know that
the weight of the Hope Diamond is equal to 8.9 grams.
Around 150 rotations
I rounded the radius to feet which is 1 foot. Then you have to get the diameter which is 1x2=2. The diameter is 2 feet. Now for the circumference, we multiply 2 by 3.14(which is pi). The answer to that is 6.28, and since we are rounding it, we get 6 feet. However, we are traveling 900 feet. Divide 900 by 6 and get 150.
