Answer:
The volume of the observatory is 497.43 
Step-by-step explanation:
i) The diameter of the floor is 10 feet. The floor is circular and has a radius,
r = 
= 5 feet.
Therefore the area of the circular floor of the observatory
= 
= 3.14159 × 
= 78.54 
ii) The observatory is made up of two parts
a) 3 foot tall cylinder
∴ volume of cylinder = × h
= 78.54 × 3
= 235.62
b) hemisphere = 
× 
= 0.6667 × 78.54 × 5 = 261.81
c) Therefore the total volume of the observatory is = a) + b)
= 235.62 + 261.81 = 497.43
The number of boats are 8; so, he needs a total of 8*126 gallons.
In order to get the partial products, first you have to decompose 126 in its hundreds, tens and ones, that is, 126 = 100 + 20 + 6. Then multiply each of this terms by 8, as follows
8*100 = 800
8*20 = 160
8*6 = 48
Finally you have to add the results of these multiplications, that is, 800 + 160 + 48 = 1008. Therefore, he needs 1008 gallons for all the boats.
The key words you should notice when looking at this word problem are “less than.” This means that the order is flipped, so “3 less than k” means “k minus 3.”
The expression for the ratio is k-3:k+3
Hope this helps
(x; y)
reflect over
x axis (x; -y)
y axis (-x; y)
therefore
(-2; 3)
x axis (-2; -3)
y axis (2; 3)
