Question

The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ....${{\left( mm \right)}^{2}}$

Answer 1

Hint: In this question, we are given height and radius of base of cylinder and find the surface area of solid cylinder in ${{\left( mm \right)}^{2}}$. Since, we are given height and radius, so we will first convert them into mm by using the formula as 1cm = 10mm. After that, we will use the formula of finding the surface area of a solid cylinder which is given by $S=2\pi r\left( r+h \right)$ where S is surface area, r is the radius of base of cylinder and h is height of cylinder.

Complete step-by-step answer:
Here, we are given a radius of the base of the cylinder as 2.0 cm which means r = 2.0 cm.
Let us first convert into millimeters.
As we know, 1cm = 10mm, therefore $2cm=2\times 10=20mm$. Hence, r becomes equal to 20mm.
\[r=20mm\cdots \cdots \cdots \cdots \cdots \left( 1 \right)\]
Height of the cylinder is given as 10cm, which means h = 10cm. Let us convert it into millimeters.
As we know, 1cm = 10mm, therefore $10cm=10\times 10=100mm$. Hence, h becomes equal to 10mm.
As we know, the surface area of the solid cylinder is the sum of curved surface area and area of two circular bases of the cylinder. So, surface area of cylinder is given as $S=2\pi rh+2\pi {{r}^{2}}$ Where $2\pi rh$ is curved surface area and $2\pi {{r}^{2}}$ is area of two circular bases.
Taking $2\pi r$ common on right side, we get:
\[S=2\pi r\left( r+h \right)\cdots \cdots \cdots \cdots \left( 2 \right)\]
Let us put values of r and h from (1) and (2) we get:
\[\begin{align}
  & S=2\times \pi \times 20\left( 20+100 \right) \\
 & \Rightarrow 40\pi \left( 120 \right) \\
 & \Rightarrow 4800\pi \\
\end{align}\]
As we know, $\pi =\dfrac{22}{7}$ so putting in above equation we get:
\[\begin{align}
  & S=4800\times \dfrac{22}{7} \\
 & S=15085.71m{{m}^{2}} \\
\end{align}\]
Hence, the surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to $15085.71m{{m}^{2}}$.

Note: Students should note that we have calculated total surface area because we were given a solid cylinder and there was no mention of finding curved surface area. Surface area into $m{{m}^{2}}$ after finding in $c{{m}^{2}}$ first by multiplying surface area obtained in $c{{m}^{2}}$ by 100 to get surface area in $m{{m}^{2}}$.