Question

3. Find the curved surface area and total surface area of a right circular
cylinder whose height and radius of the base are 20 cm and 7 cm
respectively​

Answer 1

Curved surface area and Total Surface Area of Cylinder is 880 cm² and 1188 cm² Respectively.

Given

• Height of Cylinder = 20 cm
• Radius = 7 cm

To Find

• Curved surface area
• Total Surface Area

Explanation:

FORMULA

$\\ \circ{\boxed{\underline{\sf{ Curved \ Surface \ Area_{(Cylinder)} = 2πrh }}}}$

Now, Substituting values in formula to get desired results:-

$\colon\implies{\sf{ 2πrh }} \\ \\ \\ \colon\implies{\sf{ 2 \times \dfrac{22}{ \cancel{7} } \times \cancel{7} \times 20 }} \\ \\ \\ \colon\implies{\sf{ 2 \times 22 \times 20 }} \\ \\ \\ \colon\implies{\sf{ 880 \ cm^2 }}$

So,

• Curved surface area of Cylinder is 880 cm²

FORMULA

$\\ \circ{\boxed{\underline{\sf{ Total \ Surface \ Area_{(Cylinder)} = 2πrh+2πr^2 }}}}$

After Putting values:-

$\colon\implies{\sf{ 2πrh+2πr^2 }} \\ \\ \\ \colon\implies{\sf{ 2πr(h+r) }} \\ \\ \\ \colon\implies{\sf{ 2 \times \dfrac{22}{ \cancel{7} } \times \cancel{7} (20+7) }} \\ \\ \\ \colon\implies{\sf{ 2 \times 22 (27) }} \\ \\ \\ \colon\implies{\sf{ 44 \times 27 }} \\ \\ \\ \colon\implies{\sf{ Total \ Surface \ Area_{(Cylinder)} = 1188 \ cm^2 }}$

Hence,

• The Total Surface Area of Cylinder is 1188 cm².

Answer 2

$\boxed{\fcolorbox{aqua}{gold}{Given}}$

• Height of the cylinder = 20cm.

• Radius of the cylinder = 7 cm.

$\boxed{\fcolorbox{aqua}{gold}{To \: find}}$

• Curved surface area of the cylinder.

• Total surface area of the cylinder.

$\boxed{\fcolorbox{aqua}{gold}{Solution}}$

We know the total surface area of a right circular cylinder (TSA) = $\sf{2 \pi r(r + h)}$

Now by putting the values, we get,

$\sf{\implies \: TSA = 2 \times \frac{22}{7} \times { 7}(7 + 20)}$

$\sf{\implies \: TSA = 2 \times \frac{22}{\cancel7} \times {\cancel 7} \times 27}$

$\sf{\implies \: TSA = 2 \times 22 \times 27}$

$\sf{\implies \: TSA \: = 1188}$

Now,

Curved surface area of right circular cylinder (CSA) = $\sf{2 \pi r h}$

Again,by putting the values, we get,

$\sf{\implies \: CSA \: = 2 \times \frac{22}{\cancel7} \times {\cancel 7} \times 20}$

$\sf{\implies \: CSA = 2 \times 22 \times 20}$

$\sf{\implies \: CSA = 880}$

Hence, the total surface area of the right circular cylinder = 1188 cm ² and curved surface area of the right circular cylinder = 880 cm².