Question

1. Earth is approximately a sphere of radius 6.37х106 m. what are (a) its circumference in kilometers, (b) its surface are in square kilometers, and (c) its volume in cubic kilometers?

Answer 1

As we know that circumference of the sphere is given as

`C = 4\pi R`

here we know that

`R = 6.37 * 10^6 m`

now we have

`C = 4\pi (6.37 * 10^6)`

`C = 8* 10^7 m`

`C = 8 * 10^4 km`

PART B)

surface area of the sphere is given as

`A = 4\pi R^2`

`R = 6.37 * 10^3 km`

`A = 4\pi (6.37* 10^3)^2`

`A = 5.1 * 10^8 km^2`

PART C)

Volume of the sphere is given as

`V = (4)/(3)\pi R^3`

here we have

`V = (4)/(3)\pi(6.37 * 10^3)^3`

`V = 1.1 * 10^(12) km^3`

Answer 2

Step-by-step explanation:

Given that,

Radius of Earth,
`r=6.37* 10^6\ m`

(a) It is not possible to find the circumference of the sphere. But if we consider an image of the Earth, its circumference is given by :

`C=2\pi r`

`C=2\pi * 6.37* 10^6`

`C=40.01* 10^6\ m`

`C=40.01* 10^3\ km`

(b) Surface area of a sphere is given by :

`A=4\pi r^2`

`A=4\pi (6.37* 10^6)^2`

`A=5.09* 10^(14)\ m^2`

`A=5.09* 10^(11)\ km^2`

(c) Volume of the sphere is given by :

`V=(4)/(3)\pi r^3`

`V=(4)/(3)\pi (6.37* 10^6)^3`

`V=1.082* 10^(21)\ m^3`

`V=1.082* 10^(18)\ km^3`

Hence, this is the required solution.