Surface Area Of A Sphere

To solve the problem, we need to calculate the volume and total surface area of a sphere with radius $r%20%3D%203.5%20%5C%2C%20%5Ctext%7Bcm%7D$ , using $%5Cpi%20%3D%20%5Cfrac%7B22%7D%7B7%7D$ .

1. Formula for Volume of a Sphere:

The volume of a sphere is given by:

$V%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3$

2. Substituting the Values:

$r%20%3D%203.5%20%3D%20%5Cfrac%7B7%7D%7B2%7D$

$V%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%20%5Cleft(%20%5Cfrac%7B7%7D%7B2%7D%20%5Cright)%5E3$

$%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%20%5Cfrac%7B343%7D%7B8%7D$

3. Simplifying the Volume:

$V%20%3D%20%5Cfrac%7B4%20%5Ctimes%2022%20%5Ctimes%20343%7D%7B3%20%5Ctimes%207%20%5Ctimes%208%7D$

$%3D%20%5Cfrac%7B30184%7D%7B168%7D%20%3D%20%5Cfrac%7B539%7D%7B3%7D%20%5C%2C%20%5Ctext%7Bcm%7D%5E3$

4. Formula for Surface Area of a Sphere:

Surface Area $A%20%3D%204%20%5Cpi%20r%5E2$

5. Substituting the Values:

$A%20%3D%204%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%20%5Cleft(%20%5Cfrac%7B7%7D%7B2%7D%20%5Cright)%5E2$

$%3D%204%20%5Ctimes%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%20%5Cfrac%7B49%7D%7B4%7D$

$%3D%20%5Cfrac%7B22%20%5Ctimes%2049%7D%7B7%7D%20%3D%20154%20%5C%2C%20%5Ctext%7Bcm%7D%5E2$

Final Answer:

The volume is $%5Cfrac%7B539%7D%7B3%7D%20%5C%2C%20%5Ctext%7Bcm%7D%5E3$ and the surface area is $154%20%5C%2C%20%5Ctext%7Bcm%7D%5E2$ .

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Surface Area Of A Sphere

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs