Question

Meera and Dhara have 12 and 8 coins respectively each of radius 3.5 cm and
thickness 0.5 cm. They place their coins one above the other to form solid cylinders.

Based on the above information, answer the following questions. (5 M)
(i) Curved surface area of the cylinder made by Meera is
(a) 144 cm2
(b) 132 cm2
(c) 154 cm2
(d) 142 cm2
(ii) The ratio of curved surface area of the cylinders made by Meera and Dhara is
(a) 2: 5 (b) 3: 2 (c) 1: 2 (d) 2: 7
(iii) The volume of the cylinder made by Dhara is
(a) 154 cm3
(b) 144 cm3
(c) 132 cm3
(d) 142 cm3
(iv) The ratio of the volume of the cylinders made by Meera and Dhara is
(a) 1:2 (b) 2: 5 (c) 3: 2 (d) 4: 3
(v) When two coins are shifted from Meeras cylinder to Dhara's cylinder, then
(a) Volume of two cylinder become equal
(b) Volume of Meera's cylinder> Volume of Dharas cylinder
(c) Volume of Dhara's cylinder> Volume of Meeras cylinder
(d) None of these

Answer 1

Answer:

12 + 8 total 20 coins stacked up. so net height = 20 × 0.5 = 10cm and radius = 3.5cm

height of cylinder made by Meera = 12 × 0.5 = 6cm = h1

height of cylinder made by Dhara = 8 ×0.5 = 4cm = h2

(i) curved surface area by Meera= 2πrh1 = 132 cm ² (option b)

(ii) Ratio of curved surface areas made = 2πrh1 : 2πrh2

= h1 : h2 = 6:4 = 3:2 ( option b )

(iii)volume of cylinder made by Dhara = πr²h2 = 154 cm³ (option a)

(iv)ratio of volumes = πr²h1 : πr²h2 = h1 : h2 = 3:2 (option c)

(v) 2 coins shifted from meeras cylinder to dharas cylinder. so thickness of meeras cylinder reduces by 0.5×2 = 1cm and dharas increases by 0.5×2 = 1cm. so the new thicknesses becomes h1=h2 = 5cm. from the previous subdivision we see ratio of volumes are h1:h2. therefore we can say volumes become equal ( option a)

Answer 2

Answer:

(i) Hence curved surface area of the cylinder made by Meera = 132$cm^2$

(ii)  The ratio of the curved surface area of the cylinders made by Meera and Dhara = 3:2

(iii) Volume of the cylinder made by Dhara = 154$cm^3$.

(iv) Ratio of the volume of the cylinder made by Meera and Dhara = 3:2

(v) when two coins are shifted from Meera’s cylinder to Dhara’s cylinder then volume of the two cylinders become equal

Step-by-step explanation:

Given,

The number of coins Meera has = 12

The number of coins Dhara has = 8

Radius of the coin = 3.5cm

Thickness of the coin = 0.5cm

(i) Required to find the curved surface area of the cylinder made by Meera

We Know that the curved surface area of the cylinder = $2\pi rh$, where 'r' is the radius of the cylinder and 'h' is the height of the cylinder.

Here, r = 3.5cm

Height of the cylinder made by Meera = 12 x 0.5 = 6cm

Curved surface area = 2 x  $\frac{22}{7}$ x 3.5 x 6

= $132cm^2$

Hence curved surface area of the cylinder made by Meera = 132$cm^2$

(ii) Required to find the ratio of curved surface area of the cylinders made by Meera and Dhara

Height of the cylinder made by Dhara = 8 x 0.5 = 4cm

Curved surface area of the cylinder made by Dhara = 2 x $\frac{22}{7}$ x 3.5 x 4

= 88$cm^2$

curved surface area of the cylinder made by Meera = 132$cm^2$

The ratio of curved surface area of the cylinders made by Meera and Dhara

=  132$cm^2$ : 88$cm^2$

= 3:2

Hence, the ratio of the curved surface area of the cylinders made by Meera and Dhara = 3:2

(iii) Required to find the volume of the cylinder made by Dhara

We know that,

The volume of the cylinder = $\pi r^2h$, where ‘r’ is the radius and ‘h’ is the height.

Here, r = 3.5cm

And h = 4cm

Volume of the cylinder made by Dhara = 154$cm^3$.

(iv) Required to find ratio of the volume of the cylinders made by Meera and Dhara

Height of the cylinder made by Meera = 6cm.

Height of the cylinder made by Dhara = 4cm

And radius is same for both cylinders

Ratio of their volume = $\pi r^2 x 6 : \pi r^ 2 4$

Canceling the common terms

Ratio of the volume of their cylinders = 6:4 = 3:2

Ratio of the volume of the cylinder made by Meera  and Dhara = 3:2

(v) Given, two coins are shifted from Meera’s cylinder to Dhara's cylinder

Height of  Meera’s cylinder = 10x0.5 = 5cm

Height of Dhara’s cylinder = 10 x 0.5 = 5cm

Since height and radius of both the cylinders is same, then volume also same

Hence, when two coins are shifted from Meer’s cylinder to Dhara’s cylinder then volume of the two cylinders become equal