28. Answer: 86% decrease
Step-by-step explanation:
Original Sphere has a radius of 100% → r =1
Surface Area of Original Sphere:
S.A. = 4πr²
= 4π(1)²
= 4π
New Sphere has a diameter of 75% → d = 0.75 → r = 0.375
Surface Area of New Sphere:
S.A. = 4πr²
= 4π(0.375)²
= 0.5625π
[tex]\text{\% Change} =\dfrac{New - Original}{Original}\\\\.\qquad \qquad =\dfrac{0.5625\pi -4\pi}{4\pi}\\\\.\qquad \qquad =\dfrac{-3.4375\pi}{4\pi}\\\\.\qquad \qquad =-0.86[/tex]
The negative sign represents a decrease.
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29. Answer: 72 bottles
Step-by-step explanation:
Volume of a hemisphere is:
[tex]V=\dfrac{2}{3}\pi r^3\\\\.\quad =\dfrac{2}{3}\pi (18)^3\\\\.\quad = 3888\pi[/tex]
Volume of a cylinder is:
[tex]V=\pi r^2h\\\\.\quad =\pi (3)^2(6)\\\\.\quad =54\pi[/tex]
The number of cylinders needed is:
[tex]\dfrac{3888\pi}{54\pi} = 72[/tex]
