Question

If the radius of a cylinder is 1.4cm, then the sum of the areas of its upper and lower surfaces is ____

1. 6.16 sq.cm

2. 123.2 sq.cm

3. 61.6 sq.cm

4. 12.32 sq.cm​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, we are given that the radius of the cylinder is 1.4 cm. We have to find the sum of the areas of its upper and lower surfaces.

The top and the lower surface of the cylinder is in the shape of circles. So, we need to find the area of the two circles. We'll find the area of the two circles by using the formula of the circles and then we'll add both areas in order to find the sum of the areas of its upper and lower surfaces.

$\Large {\underline { \sf \orange{Explication \: of \: steps :}}}$

$\bf \red { \dag }$ Area of the upper surface :

We know that,

$\bigstar \: \boxed{\sf { Area_{(Circle)} = \pi {r}^{2} }}$

$\longrightarrow \sf {Area_{(Upper \: Surface)} = \dfrac{22}{7} \times {(1.4)}^{2} \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Upper \: Surface)} = \dfrac{22}{7} \times 1.4 \times 1.4 \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Upper \: Surface)} = \dfrac{\cancel{22}}{\cancel{7}} \times \dfrac{\cancel{14}}{\cancel{10}} \times \cancel{\dfrac{14}{10}} \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Upper \: Surface)} = 11 \times \dfrac{2}{5} \times \dfrac{7}{5} \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Upper \: Surface)} = \dfrac{154}{25} \: {cm}^{2} }$

$\longrightarrow$ ❝ $\boxed{ \sf \orange { Area_{(Upper \: Surface)} = 6.16 \: {cm}^{2} }}$ ❞

$\bf \red { \dag }$ Area of lower surface :

We know that,

$\bigstar \: \boxed{\sf { Area_{(Circle)} = \pi {r}^{2} }}$

$\longrightarrow \sf {Area_{(Lower \: Surface)} = \dfrac{22}{7} \times {(1.4)}^{2} \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Lower \: Surface)} = \dfrac{22}{7} \times 1.4 \times 1.4 \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Lower \: Surface)} = \dfrac{\cancel{22}}{\cancel{7}} \times \dfrac{\cancel{14}}{\cancel{10}} \times \cancel{\dfrac{14}{10}} \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Lower \: Surface)} = 11 \times \dfrac{2}{5} \times \dfrac{7}{5} \: {cm}^{2} }$

$\longrightarrow \sf {Area_{(Lower \: Surface)} = \dfrac{154}{25} \: {cm}^{2} }$

$\longrightarrow$ ❝ $\boxed{ \sf \orange { Area_{(Lower \: Surface)} = 6.16 \: {cm}^{2} }}$ ❞

$\bf \red { \dag }$ Sum of the areas of its upper and lower surfaces :

$\longrightarrow \sf { Sum = (6.16 + 6.16) \: {cm}^{2} }$

$\longrightarrow$ ❝ $\boxed{ \sf \orange { Sum = 12.32 \: {cm}^{2} }}$ ❞ $\orange {\bigstar}$

❝ Therefore, the sum of the areas of its upper and lower surfaces is $\mathfrak {\pmb{\gray { 12.32 \: {cm}^{2} }}}$. ❞

Answer 2

Given :

• Shape = Cylinder
• Radius of Cylinder = 1.4cm

To Find :

• The Sum of the areas of its upper and lower surfaces.

Solution :

✰ As we know that, The upper and lower surfaces of a Cylinder are in the shape of Circle and in the Question it is asked that we have to find the sum of area of its upper and lower surfaces. So we will find the area of the upper and lower surfaces separately and then we will add them .

⠀⠀

⟼ Area of Upper Surface = πr²

⟼ Area = 22/7 × (1.4)²

⟼ Area = 22/7 × 14/10 × 14/10

⟼ Area = 22/7 × 196/100

⟼ Area = 4312/700

⟼ Area = 6.16cm²

⠀⠀

Now,

⟼ Area of Lower Surface = πr²

⟼ Area = 22/7 × (1.4)²

⟼ Area = 22/7 × 14/10 × 14/10

⟼ Area = 22/7 × 196/100

⟼ Area = 4312/700

⟼ Area = 6.16cm²

⠀⠀

And,

⟹ Sum of Areas of both surfaces

⟹ 6.16 + 6.16

⟹ 12.32cm²

Thus Correct Option is 4 i.e 12.32cm²

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★ Additional Info :

Formulas Related to Circle:

• Circumference of Circle = 2πr
• Area of Circle = πr²
• Diameter of Circle = 2r
• Radius of Circle = D/2

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