Question

Dev was doing an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius R = 7 cm and height 10 cm. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from A to B equal to 3.40 cm

i. What is the approximate radius of the sphere?
a. 7 cm b. 5 cm c. 4 cm d. 3 cm

ii. What is the volume of the cylinder?
a. 700 cm³ b. 500 cm³ c. 1540 cm³ d. 2000 cm³

iii. What is the volume of the sphere?
a. 700 cm³b. 600 cm³ c. 500 cm³ d. 523.8 cm³

iv. How many litres water can be filled in the full container?( Take 1 litre=1000 cm³)
a. 1.50 b. 1.44 c. 1.54 d. 2

v. What is the surface area of the sphere?
a. 314.3 m² b. 300 m² c. 400 m² d. 350 m²


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Answer 1

Refer to the attachment.

Hope this helps...

Answer 2

Radius of the sphere (r) is (b) 5 cm.

Volume of the half filled cylinder is (c) 1540 cm³.

Volume of sphere is (d) 523.8 cm³.

Volume of the complete filled cylinder is (c) 1.54 litre.

Surface area of the sphere is (a) 314.3 cm².

Given:

Radius of the cylinder (R) = 7 cm

Height of the cylinder (h) = 10 cm

To find:

1. Radius of the sphere (r).
2. Volume of the half filled cylinder.
3. Volume of sphere.
4. Volume of the complete filled cylinder.
5. Surface area of the sphere.

Explanation:

We have been given in the question that when a sphere is dropped in a half filled cylinder, the rise in water level is height (h') = 3.4 cm

Solution 1

From Archimedes Principle, we know that the volume of water that will rise in the cylinder, will be equal to the volume of the sphere .

Mathematically,

Volume of water rise $=$ Volume of the sphere

                       πR²h'   $=$  4/3 π r³

              Hence,     $r^{3} = \frac{3R^{2}h' }{4}$

Substituting the values, we get

                               $r^{3} = \frac{3(7)^{2} (3.4) }{4}$

                                $r^{3} = 125$

Therefore, $r=5cm$

Solution 2

We have the given information, that the cylinder is filled up half.

Hence, $height$ $= \frac{h}{2} = 5 cm$  $and$  $radius = 7 cm$

Therefore,

Volume of the cylinder $=$ πR²H          

                                      $=$   $\frac{22}{7}(7)^{2}(5)$

                                      $=1540 cm^{3}$  

Solution 3

We have calculated, radius of the sphere (r) = 5 cm

Therefore,

The volume of the sphere = 4/3 π r³

Substituting the values, we get  $= \frac{4}{3}(\frac{22}{7})(5)^{3}$

                                                     $= 523.8cm^{3}$

Solution 4

Since, we have height of the full cylinder, that is h = 10 cm

and radius of the cylinder (R) = 7 cm

Therefore, the volume of the cylinder will be = πR²h  

Substituting the given values, we get $= \frac{22}{7}(7)^{2} (10)$

                                                               $=1540cm^{3}$

Given that,

1 litre = 1000 cm³  ;

Therefore,

1540 cm³ = 1.54 L

Solution 5

We know the surface area of the sphere = 4πr²

where, radius of the sphere r = 5 cm

Hence,

Surface area $= 4(\frac{22}{7})(5)^{2}$

                      $=314.3m^{2}$

Final answer:

Hence,

1. Radius of the sphere (r) is (b) 5 cm.
2. Volume of the half filled cylinder is (c) 1540 cm³.
3. Volume of sphere is (d) 523.8 cm³.
4. Volume of the complete filled cylinder is (c) 1.54 litre.
5. Surface area of the sphere is (a) 314.3 cm².