Question

A petrol tank is a cylinder of base diameter 24 cm and length 20 cm fitted with conical ends each of height 8 cm. Determine the capacity of the tank.

Answer 1

Answer:

Volume of the cylindrical portion of the tank= TTr2h

=22/7 * (28/2)2 * 24cm3 

= 14784cm3

Volume of 2 conical ends

=2 (1/3 TTr2h) =2/3 TTr2h =2/3 * 22/7 *14*14 * 9cm3

=3696cm3

Therefore, capacity of the tank= 14784cm3 + 3696cm3= 18480cm3

Thus, capacity of the tank= 18480cm3

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Step-by-step explanation:

Answer 2

Answer:

The capacity of the tank is approximately 11,305.5cm³ (cubic centimeters) .

Step-by-step explanation:

The petrol tank consists of a cylindrical portion and two conical ends. We can calculate the volume of each portion separately and then add them up to find the total capacity of the tank.

The radius of the cylinder is half its diameter, hence its volume is given by

$r = \frac{ 24}{2 }= 12 cm.$

The cylinder measures 20 centimetres in length. As a result, the cylindrical portion's volume is:

$Vcyl = πr^2h$

$= π(12)^2(20)$

$= 9,072π \: cubic \: centimeters$

Each conical end's volume is shown by a radius of 12 cm (since the diameter of the base is the same as that of the cylinder). Each conical end has a height of 8 cm. Hence, each conical end's volume is as follows:

$Vcone = \frac{1}{3}πr^2h$

$= \frac{1}{3} π(12)^2(8)$

$= \frac{ 1,152π}{3} cubic \: centimeters$

Total volume of the tank:

The tank consists of a cylindrical portion and two conical ends, so the total volume is:

$Vtotal = Vcyl + 2Vcone$

$= 9,072π + 2( \frac{1,152π}{3})$

$= 9,072π + \frac{2,304π}{3}$

$= \frac{10,752π}{3} cubic \: centimeters$

≈ 11,305.5 cubic centimeters

Therefore, the capacity of the tank is approximately 11,305.5 cubic centimeters.

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