Question

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It is in the attachment ​​
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Answer 1

Answer:

(i) Radius = 7cm  Area of the circular surface $= 308$ $cm^2$

(ii) Radius = 3.5cm  Area of the circular surface $= 77$ $cm^2$

(iii) Radius = 14cm  Area of the circular surface $= 1,232$ $cm^2$

(iv) Radius = 2.8cm  Area of the circular surface $= 49.28$ $cm^2$

Step-by-step explanation:

Area of circular surface of any Cylinder is twice the area of circle of given radius.  This is because, cylinders have circular surface at both of it's ends.

(i) Radius = 7cm

Area of the circular surface:

$2$ . (π . $7^2$) $cm^2$

$=2$ . $\frac{22}{7}$ . $7^2$ $cm^2$

$=2$ . $22$ . $7$ $cm^2$

$= 308$ $cm^2$

(ii) Radius = 3.5cm

Area of the circular surface:

$2$ . [π . $(3.5)^2$] $cm^2$

$=2$ . $\frac{22}{7}$ . $\frac{35^2}{10^2}$ $cm^2$

$=2$ . $22$ . $\frac{5 . 35}{100}$ $cm^2$

$= 11 . 7$ $cm^2$

$= 77$ $cm^2$

(iii) Radius = 14cm

Ratio of radii of (i) and (ii) = 1:2  [∵ radius in (i) is 7 cm and that in (ii) is 14 cm]

∴ The ratio of the required Area = 1 squared : 2 squared = 1:4

∴ Area of the circular surface with radius of 14 cm is 4 times that of with radius 7 cm, that is, four times $308$ $cm^2$ $= 1,232$ $cm^2$

(iv) Radius = 2.8cm

Ratio of radii of (i) and (ii) = 70:28 = 5:2  [∵ radius in (i) is 7 cm and that in (ii) is 2.8 cm]

∴ The ratio of the required Area = 5 squared : 2 squared = 25:4

∴ Area of the circular surface with radius of 2.8 cm is $\frac{4}{25}$ times that of with radius 7 cm, that is, $\frac{4}{25}$ times $308$ $cm^2$ $= 49.28$ $cm^2$