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 
Vsphere=(4/3)pir^3
Voriginal=(4/3)pir^3
when radius is multiplied by 4
replace r with 4r
Vnew=(4/3)pi(4r)^3
Vnew=(4/3)pi(64r^3)
Vnew=(64)(4/3)pir^3
Vnew=(64)(Voriginal)
the volume is 64 times the original
Answer: x = 33
Step-by-step explanation:
Subtract 2/11x from both sides
Subtract 4 from both sides
Multiply both sides by 11/4
Answer:
=a^32
Step-by-step explanation:
(a^8)^4= a^8.4
=a^8.4