Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 4500/3 πin3. One day, his sink clogged. He has to use one of

Question

Anthony has a sink that is shaped like a half-sphere. The sink has a volume of 4500/3 πin3. One day, his sink clogged. He has to use one of two cylindrical cups to scoop the water out of the sink. The sink is completely full when Anthony begins scooping. One cup has a diameter of 6 in. And a height of 14 in. How many cups of water must Anthony scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. One cup has a diameter of 10 in. And a height of 12 in. How many cups of water must he scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number.

in progress 0
Hồng Cúc 4 years 2021-09-04T09:26:50+00:00 1 Answers 65 views 0

Answers ( )

  1. trucchi
    0
    2021-09-04T09:28:21+00:00
    Reply

    Answer:

    Scoops = 12 — cup 1

    Scoops = 5  — cup 2

    Step-by-step explanation:

    Given

    Hemisphere

    Volume = \frac{4500\pi}{3}\ in^3

    Cup 1

    Height = 14\ in

    Diameter = 6\ in

    Cup 2

    Height = 12\ in

    Diameter = 10\ in

    Required: How many scoop of each?

    For cup 1

    Calculate the volume

    Volume = \pi r^2h

    Where

    h = 14

    r = \frac{1}{2} * 6 = 3

    Volume = \pi r^2h

    Volume = \pi * 3^2 * 14

    Volume = \pi * 126

    Volume = 126\pi

    Divide the volume of the hemisphere by the calculated volume of cup 1

    Scoops = \frac{4500\pi}{3} / 126\pi

    Scoops = \frac{4500\pi}{3} * \frac{1}{126\pi}

    Scoops = \frac{1500\pi}{1} * \frac{1}{126\pi}

    Scoops = \frac{1500\pi}{126\pi}

    Scoops = 12 — approximated

    For cup 2

    Calculate the volume

    Volume = \pi r^2h

    Where

    h =12

    r = \frac{1}{2} * 10 = 5

    Volume = \pi r^2h

    Volume = \pi * 5^2 * 12

    Volume = \pi * 300

    Volume = 300\pi

    Divide the volume of the hemisphere by the calculated volume of cup 2

    Scoops = \frac{4500\pi}{3} / 300\pi

    Scoops = \frac{4500\pi}{3} * \frac{1}{300\pi}

    Scoops = \frac{1500\pi}{1} * \frac{1}{300\pi}

    Scoops = \frac{1500\pi}{300\pi}

    Scoops = 5

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )