Question

The length of the equator of the globe is $44$cm. Find its surface area.

Answer 1

Hint: The key point to solve this question is that the length equator is the circumference of the globe.
So, The circumference of the circle is $2\pi r$, where $r$ is the radius.
We find the radius using the circumference and using the formula of the surface area for the sphere, we find the surface area of the globe.
The surface area of the circle is $4\pi {r^2}$, where $r$ is the radius.

Complete step-by-step answer:
Given the length of the equator of the globe is $44$cm.
The Equator is an imaginary line perpendicular to the rotational axis. It is equidistant from the North and South Poles and divides the globe into the Northern Hemisphere and the Southern Hemisphere.
The length of the equator is the circumference of the circle.
The circumference of the circle is $2\pi r$, where $r$ is the radius.
Substitute the circumference of the circle is $44$cm.
$44 = 2\pi r$
$ \Rightarrow 44 = 2 \times \dfrac{{22}}{7} \times r$
$ \Rightarrow \dfrac{{44 \times 7}}{{2 \times 22}} = r$
$ \Rightarrow r = 7$
The radius of the globe is $7$cm.
The surface area of the globe is $4\pi {r^2}$, where $r$ is the radius.
Substitute $r = 7$into the formula,
The Surface Area=$4\pi {\left( 7 \right)^2}$
The Surface Area=$4 \times \dfrac{{22}}{7} \times 49$
The Surface Area=$616$cm$^2$

Final Answer: The Surface Area of the globe is $616$cm$^2$.

Note:
Students have to understand that the length of the equator is the same as the circumference of a circle and the surface area of the globe is the same as the surface area of the sphere.
Here, are some formulas for the students,
Area of the circle: $\pi {r^2}$
Circumference of the circle: $2\pi r$
Surface Area of sphere: $4\pi {r^2}$
Volume of sphere: $\dfrac{4}{3}\pi {r^3}$