Samir’s family has decided to purchase an above-ground cylindrical swimming pool for his backyard. The best space that they have for a pool measures 360 cm across. The tallest pool that they can buy is 120 cm high.
a) What is the volume of the largest pool that they can buy? Give your answer in cubic centimeters.
b) The walls on the pool inflate to be 10 cm thick, but the bottom of the pool is just a thin piece of vinyl. What would the full capacity of this pool be?
c) The manufacturer’s instructions warn that the pool should only be filled to 90% of its capacity. How much water would it take to fill the pool 90%? Give your answer in liters.
Answers
12208320 cm³ is volume of pool , Capacity = 10889520 cm³ and 9800.568 litres water required to fill swimming pool
Step-by-step explanation:
Radius = ½ diameter
Radius = ½ x 360 cm
Radius = 180 cm
Volume of cylinder = πr²h
Volume = 3.14 x 180² x 120 cm³
Volume = 12208320 cm³
Volume =12.21 m³ (because 1 000 000 cm³ = 1 m3)
Capacity of pool = volume of inside of pool
Diameter of inside of pool = diameter of outside of pool – thickness of 2 walls
Diameter of inside of pool = 360 cm – (2 x 10) cm
Diameter of inside of pool = 340 cm
Radius = ½ of diameter
Radius = ½ x 340 cm
Radius = 170 cm
Volume of inside of pool (capacity) = 3.14 x 170² x 120
Capacity = 10889520 cm³
10.89 m³
90% of capacity = 10889520 cm³ x (90/100)
= 9800568 cm³ or
9800.568 litres
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