Math, asked by vidhidave2173, 10 months ago

A test tube has lower part as hemisphere and upper part cylindrical with the same radius. If 6cm³ water is added to the test tube,it will be completely filled. But if 2000/3 cm³ of water is added, 5 cm height will remain empty. Find the radius of the tube and the height of the cylindrical part. (π = 22/7)

Answers

Answered by stefangonzalez246
0

Radius of the tube is 6.48 cm and height of the cylindrical part is 4.5203 cm

Step-by-step explanation:

Given Data

The lower part of a test tube is hemisphere and upper part as cylinder with same radius

Volume of the container = 6 cm³

If 2000 /3 cm³ of water is added 5 cm height will remain empty

π = 22 ÷ 7

Find the radius and height of the cylindrical part

Total volume = Volume of the cylinder + volume of the hemisphere

Total volume = πr²h + (2÷3) πr³

Total volume = πr² (h + (2÷3 r)

Substitute the values in above equation

6 cm³ = (22÷7) r² (h + (2÷3)r )

6 cm³ = 3.14 r² (h+0.67 r)    

6÷3.14 = r² (h+0.67 r)

1.909 = r²h+0.67 r³ ------------> 1

If (2000÷3) cm³ of water is added , 5 cm height will remain empty and that can be written as

(2000 ÷ 3) = (volume of the cylinder - 5 cm ) + volume of hemisphere

(2000 ÷ 3) = (πr²h - 5) + (2÷3) πr³

(2000 ÷ 3) = πr²(h-5+ (2÷3)r)

(2000 ÷ 3) = (πr² ÷ 3)( 3 h-15+2 r)

2000 =  (πr²)( 3 h-15+2 r)  

2000 = 3.14 πr²(3 h-15+2 r)

2000÷π = r²( 3 h-15+2 r)

636.61 = r²(3 h-15+2 r)

636.61 = 3 hr² -15 r² +2 r³ ----------------> 2

From equation ( 1 )

h = (1.909-0.67 r³) ÷r² ----------------> 3

Substitute the value of h in equation 2

636.61 = 3 r² ((1.909-0.67 r³) ÷r²) -15 r² + 2 r³       (cm)

636.61 = 3(1.909-0.67 r³) -15 r² + 2 r³

636.61 = 5.727 - 2.0 r³ - 15 r² +2 r³

636.61 = 5.727 +2 r³

636.61 - 5.727 = 2 r³

630.883 = 2 r³

r³ = 630.883 ÷ 2

r³ = 315.441 cm

r = 6.48 cm

substitute the value of r in equation 3

h = (1.909 -0.67(6.807)³) ÷ (6.807)² cm

h = (209.436) ÷ 46.335 cm

h = 4.5203 cm

Radius of the tube is 6.48 cm and height of the cylindrical part is 4.5203 cm

To learn more ....

1. https://brainly.in/question/6559098

2. https://brainly.in/question/11798006

 

 

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