[Mohammad Adnaan]

Circumference, area, and volume are different measurements associated with a sphere, which is a three-dimensional geometric shape in which all points on its surface are equidistant from its center. Here’s an explanation of each of these measurements:

1. Circumference of a Sphere:

The circumference of a sphere refers to the distance around the outer boundary or “edge” of the sphere. It is similar to the concept of perimeter for two-dimensional shapes. The circumference of a sphere can be calculated using the formula:

Circumference = 2πr

where “π” represents the mathematical constant pi (approximately 3.14159) and “r” represents the radius of the sphere, which is the distance from the center of the sphere to any point on its surface.

2. Area of a Sphere:

The area of a sphere refers to the total surface area covered by the sphere. It represents the sum of all the individual areas of the infinitesimally small points that make up the surface of the sphere. The formula to calculate the surface area of a sphere is:

Area = 4πr²

where “π” is pi and “r” is the radius of the sphere.

3. Volume of a Sphere:

The volume of a sphere represents the amount of three-dimensional space enclosed by the sphere. It measures the total capacity or amount of material that the sphere can hold. The formula to calculate the volume of a sphere is:

Volume = (4/3)πr³

Here, “π” represents pi, and “r” is the radius of the sphere.

In summary, the circumference of a sphere refers to the distance around its outer boundary, the area represents the total surface area of the sphere, and the volume measures the amount of space enclosed by the sphere. These measurements are essential in various mathematical and real-world applications involving spheres, such as architecture, engineering, physics, and more.

[Mohammad Adnaan]

To find the area covered by grass in the nursery school playground, we need to calculate the total area of the playground and subtract the areas occupied by the swings and the paths.

Given information:

Length of the playground = 160 m

Width of the playground = 80 m

Area of the swings = 80 m × 80 m

Width of the path = 1.5 m

Step 1: Calculate the total area of the playground.

Total area = Length × Width

Total area = 160 m × 80 m

Total area = 12,800 square meters

Step 2: Calculate the area occupied by the swings.

Area of the swings = 80 m × 80 m

Area of the swings = 6,400 square meters

Step 3: Calculate the area occupied by the paths.

Since there is a 1.5 m wide path parallel to the width and another parallel to the remaining length, we need to calculate the area of both paths and subtract them from the total.

Area of the path parallel to the width:

Length of the path = Length of the playground = 160 m

Width of the path = 1.5 m

Area of the path parallel to the width = Length of the path × Width of the path

Area of the path parallel to the width = 160 m × 1.5 m

Area of the path parallel to the width = 240 square meters

Area of the path parallel to the remaining length:

Length of the path = Width of the playground = 80 m

Width of the path = 1.5 m

Area of the path parallel to the remaining length = Length of the path × Width of the path

Area of the path parallel to the remaining length = 80 m × 1.5 m

Area of the path parallel to the remaining length = 120 square meters

The total area of the paths = Area of the path parallel to the width + Area of the path parallel to the remaining length

Total area of the paths = 240 square meters + 120 square meters

The total area of the paths = 360 square meters

Step 4: Calculate the area covered by grass.

Area covered by grass = Total area – Area of the swings – Total area of the paths

Area covered by grass = 12,800 square meters – 6,400 square meters – 360 square meters

Area covered by grass = 6,040 square meters

Therefore, the area covered by grass in the nursery school playground is 6,040 square meters.