Question

Please Help Me........

Answer 1

The formula for the volume of a sphere is V=(4/3)πr³.  We will only need half of this, so our formula is V=(1/2)(4/3)πr³=(4/6)πr³=(2/3)πr³.  Since the diameter of the sink is 20 in, the radius is half of that or 10 in.  Substituting that in, we have:
V=(2/3)π(10³)=(2/3)(1000)π=2000π/3 in³.

The formula for the volume of the conical cup is V=(1/3)πr²h.  Our radius is 1/2 of the 8 in diameter, or 4 in.  Using our information we have V=(1/3)π(4²)(6)=(1/3)π(96)=32π in³.

To find out how many cups it will take to empty the sink, we divide the volume of the sink by the volume of the cup:
$\frac{2000\pi}{3} \div 32\pi \\ \\=\frac{2000\pi}{3} \div \frac{32\pi}{1} \\ \\=\frac{2000\pi}{3} * \frac{1}{32\pi} \\ \\=\frac{2000\pi *1}{3*32\pi} \\ \\=\frac{2000*1}{3*32}=\frac{2000}{96} \approx 21$

The volume of the cylindrical cup is given by the formula V=πr²h.  Our radius is half of the diameter of 4, or 2 in.  Using our information we have V=π(2²)(6)=24π in³.  To determine how many cups it would take to empty the sink we divide the volume of the sink by the volume of the cup:
$\frac{2000\pi}{3} \div 24\pi \\ \\=\frac{2000\pi}{3} \div \frac{24\pi}{1} \\ \\=\frac{2000\pi}{3} * \frac{1}{24\pi} \\ \\=\frac{2000\pi *1}{3*24\pi}=\frac{2000*1}{3*24}=\frac{2000}{72} \approx 28$