Question

Dev was experimenting to find the radius r of a sphere. For this, he took a cylindrical container with a radius R = 7 cm and a height of 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 liters of water can be filled in the full container?( Take 1 litre=1000 cm³)
a. 1.50 b. 1.44 c. 1.54 d. 2


NO SPAMMERS ALLOWED

Answer 1

Answer:

i b.5

ii 1540

iii 523.8

iv 1.54

Answer 2

Given:

Dev was experimenting to find the radius r of a sphere. For this, he took a cylindrical container with a radius R = 7 cm and a height of 10 cm. He filled the container almost half with water

Now he dropped the yellow sphere in the container. Now he observed  the water level in the container raised from A to B equal to 3.40 cm

To find:

What is the approximate radius of the sphere?

What is the volume of the cylinder?

What is the volume of the sphere?

How many litres of water can be filled in the full container?( Take 1 litre=1000 cm³)

Solution:

Finding the approximate radius of the sphere:

The volume of water at point A,

= $\frac{1}{2} \times Volume \:of\: the \:cylinder$ [since the container is half-filled with water at a point A]

= $\frac{1}{2} \times \pi r^2 h$

= $\frac{1}{2} \times \frac{22}{7} \times 7^2 \times 10$

= $\frac{1}{2} \times 1540$

= $\bold{770 \:cm^3}$

The volume of water at point B,

= [Volume at point A] + [Volume of the rise in water]

= $770 + [\frac{22}{7} \times 7^2 \times 3.4]$

= $770 + 523.6$

= $\bold{1293.6\:cm^3}$

The volume of the sphere = [Volume at point B] - [Volume at point A]

⇒ $\frac{4}{3} \pi r^3 = 1293.6 - 770$

⇒ $\frac{4}{3} \pi r^3 = 523.6$

⇒ $r^3 = \frac{523.6 \times 3 \times 7}{22 \times 4}$

⇒ $r^3 = 124.95$

⇒ $r = 4.9$ ≈ $5\:cm$

Thus, the approximate radius of the sphere is → 5 cm.

Finding the volume of the cylinder:

The volume of the cylindrical container,

= $Volume \:of\: the \:cylinder$  

= $\pi r^2 h$

= $\frac{22}{7} \times 7^2 \times 10$

= $1540\:cm^3$

Thus, the volume of the cylinder is → 1540 cm³.

Finding the volume of the sphere:

The radius of the sphere = 5 cm

∴ The volume of the sphere = $\frac{4}{3} \pi r^3 = \frac{4}{3}\times \frac{22}{7} \times 5^3 = 523.8 \:cm^3$

Thus, the volume of the yellow sphere is → 523.8 cm³.

Finding the litres of water filled in the full container:

The volume of water that can be filled in the full container is,

= Volume of the cylindrical container

= $Volume \:of\: the \:cylinder$  

= $\pi r^2 h$

= $\frac{22}{7} \times 7^2 \times 10$

= $1540\:cm^3$

we know 1 litre = 1000 cm³

= $\frac{1540}{1000}\:litres$

= $1.54 \:litres$

Thus, 1.54 litres of water can be filled in the full container.

----------------------------------------------------------------------------------------

Also View:

A design for a traffic cone is shown below. In order for it to have a solid foundation, the designers want to make the base and cone out of solid plastic. If the plastic is $0.75 per cubic cm, how much will it cost them to make 5 cones?

brainly.in/question/27019371  

Rachel an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. the diameter of the model is 3cm and its length is 12cm. If each come has a height of 2cm. find the volume of air contained in the model that Rachel made.

brainly.in/question/14315681  

Mathematics teacher of a school took her 10th standard students to show Tajmahal.  

The teacher said in this monument one can find a combination of solid figures.  

(i)Write the formula to find the volume of a hemispherical dome.  

(ii)Find the lateral surface area of 4 pillars if the height of each pillar is 20m and radius of the base is 1.4m.  

(iii)How much is the volume of 2 small hemispheres each of radius 2.1m?  

(iv)How much cloth material will be required to cover 1 big dome of radius 4.2m?  

(v)What is the ratio of the sum of volumes of four hemispheres of radius 1m each to the volume of a sphere of radius 2m?

brainly.in/question/30261412