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Mensuration | Mensuration Exercise 18.3

Question 11

A rectangular piece of a tin of size 30 cm × 18 cm is rolled in two ways, once along its length (30 cm) and once along with its breadth. Find the ratio of volumes of two cylinders so formed.

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Given,

Size of rectangular tin plate = 30 cm × 18 cm

(i) When rolled along its length (30 cm),

Then, the circumference of the circle so formed = 30 cm

Radius(r1) = C/2π = (30 x 7)/ (2 x 22) = 105/22 cm

And height (h1) = 18 cm

Then, volume = πr12h1 = π x (105/22)2 x (18) cm3

If it is rolled along its breadth (18 cm) then,

Circumference = 18 cm

So, radius (r2) = C/2π = (18 x 7)/ (2 x 22) = 63/22 cm

And height (h2) = 30 cm

Then, volume = πr22h2 = π x (63/22)2 x (30) cm3

Now, ratio between the two volumes

= π x (105/22)2 x (18) : π x (63/22)2 x (30)

= (105/22)2 x (18) : (63/22)2 x (30)

= 5 : 3

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Our top 5% students will be awarded a special scholarship to Lido.

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Question 11

A rectangular piece of a tin of size 30 cm × 18 cm is rolled in two ways, once along its length (30 cm) and once along with its breadth. Find the ratio of volumes of two cylinders so formed.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

Given,

Size of rectangular tin plate = 30 cm × 18 cm

(i) When rolled along its length (30 cm),

Then, the circumference of the circle so formed = 30 cm

Radius(r1) = C/2π = (30 x 7)/ (2 x 22) = 105/22 cm

And height (h1) = 18 cm

Then, volume = πr12h1 = π x (105/22)2 x (18) cm3

If it is rolled along its breadth (18 cm) then,

Circumference = 18 cm

So, radius (r2) = C/2π = (18 x 7)/ (2 x 22) = 63/22 cm

And height (h2) = 30 cm

Then, volume = πr22h2 = π x (63/22)2 x (30) cm3

Now, ratio between the two volumes

= π x (105/22)2 x (18) : π x (63/22)2 x (30)

= (105/22)2 x (18) : (63/22)2 x (30)

= 5 : 3

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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