Question 1: The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm^{3} = 1l)

**Answer:** Given; circumference = 132 cm, h = 25 cm

Circumference `= 2 π r`

Or, `132 = 2 πr`

Or, `r = (132 xx7)/(2 xx 22) = 21` cm

Volume of cylinder `= π r^2\h= (22/7) xx 21^2\ xx 25`

`= 34650` cubic cm `= 34650/1000` litre`= 34.65` litre

Question 2: The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm^{3} of wood has a mass of 0.6 g.

**Answer:** Given; R = 14 cm, r = 12 cm, h = 35 cm

Volume of pipe `= π R^2\h – π r^2\h`

`= π h (R^2\ - r^2)`

`= (22/7) xx 35 (14^2 - 12^2)`

`= 110 (14 + 12)(14 – 12)`

`= 110 xx 26 xx 2 = 5720` cubic cm

Mass `= 5720 xx 0.6\ g = 3432\ g`

Question 3: A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

**Answer:** Rectangular can: `l = 5\ cm, `b = 4 \cm, `h = 15\ cm`

Volume of cubcoid `= l xx b xx h`

`= 5 xx 4 xx 15 = 300` cubic cm

Cylindrical can: r = 35 cm, h = 10 cm

Volume of cylinder `= π r^2\ h`

`= (22/7) xx 35^2\xx 10`

`= 385` cubic cm

Difference `= 385 – 300 = 85` cubic cm

Question 4: If the lateral surface of a cylinder is 94.2 cm^{2} and its height is 5 cm, then find (i) radius of its base (ii) its volume. (Use π = 3.14)

**Answer:** Given; curved surface area of cylinder = 94.2 sq cm, h = 5 cm

CSA of cylinder `= 2 π rh`

Or, `94.2 = 2 xx 3.14 xx r xx 5`

Or, `r = 94.2/(2 xx 3.14 xx 5) = 3` cm

Now, volume of cylinder `= π r^2\ h`

`= 3.14 xx 3^2\ xx 5 = 141.30` cubic cm

Question 5: It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m^{2}, find

(i) inner curved surface area of the vessel,

(ii) radius of the base,

(iii) capacity of the vessel.

**Answer:** Cost = Rs. 2200, rate = Rs. 20 per sq m, h = 10 m

Curved surface area = Cost/Rate

`= 2200/20 = 110` sq cm

CSA of cylinder `= 2 π rh`Or, `110 = 2 xx (22/7) xx r xx 10`

Or, `r = (110 xx 7)/(2 xx 22 xx 10) = 1.75` cm

Now, volume of cylinder `= π r^2\ h`

`= (22/7) xx (1.75)^2\ xx 10 = 96.25` cubic m

Question 6: The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

**Answer:** Capacity = 15.4 litre = 15400 cubic cm, h = 1 m = 100 cm

Volume of cylinder `= π r^2\ h`

Or, `15400 = (22/7) xx r^2\xx 100`

Or, `r^2= (15400 xx 7)/(22 xx 100) = 49`

Or, `r = 7` cm

Now, total surface area of cylinder `= 2 π r(r + h)`

`= 2 xx (22/7) xx 7 (7 + 10)`

`= 2 xx 22 xx 17 = 748` sq cm

Question 7: A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

**Answer:** Radius of pencil = 3.5 mm, h = 14 cm = 140 mm

Volume of pencil `= π r^2\h`

`= (22/7) xx (3.5)^2\ xx 140 = 5390` cubic mm

Radius of lead = 0.5 mm, h = 140 mm

Volume of lead `= π r^2\ h`

`= (22/7) xx (0.5)^2\ xx 140 = 110` cubic mm

Hence, volume of wood `= 5390 – 110 = 5280` cubic mm

Question 8: A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?

**Answer:** Given; r = 3.5 cm, h = 4 cm

Volume of cylinder `= π r^2\ h`

`= (22/7) xx (3.5)^2\ xx 4 = 154` cubic cm

Volume of 250 bowls `= 250 X 154 = 38500` cubic cm = 38.5 litre

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