Question - 1 : -
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? [NCERT]

Answer - 1 : - In first case, in a rectangular container of softdrink, the length of base = 5 cm
and Width = 4 cm
Height = 15 cm
∴ Volume of soft drink = lbh= 5 x 4 x 15 = 300 cm³
and in second case, in a cylindrical container, diameter of base = 7 cm

Thesoft drink in second container is greater and how much greater = 385 cm – 380cm² = 85 cm²

Question - 2 : - The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such pillars? [NCERT]

Answer - 2 : - Radius of each pillar (r) = 20 cm

Question - 3 : - The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find themass of the pipe, if 1 cm³ of wood has a mass of 0.6 gm.[NCERT]

Answer - 3 : - Inner diameter of a cylindrical wooden pipe = 24 cm

Question - 4 : - If the lateral surface of a cylinder is 94.2 cm² andits height is 5 cm, find:
(i) radius of its base
(ii) volume of the cylinder [Use π = 3.14] [NCERT]

Answer - 4 : - Lateral surface area of a cylinder = 94.2 cm2

Question - 5 : - The capacity of a closed cylindrical vessel of height1 m is 15.4 litres. How many square metres of metal sheet would be needed tomake it? [NCERT]

Answer - 5 : - The capacity of a closed cylindrical vessel = 15.4 l

Question - 6 : - A patient in a hospital is given soup daily in acylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a heightof 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?[NCERT]

Answer - 6 : - Diameter of the cylindrical bowl = 7 cm
∴ Radius (r) = 7/2cm
Level of soup in it = 4 cm
∴ Volume of soup in one bowlfor one patient

Question - 7 : - A hollow garden roller, 63 cm wide with a girth of 440cm, is made of 4 cm thick iron. Find the volume of the iron.

Answer - 7 : - Width of hollow cylinder (A) = 63 cm
Girth = 440 cm

Question - 8 : - The cost of painting the total outside surface of aclosed cylindrical oil tank at 50 paise per square decimetre is ₹ 198. Theheight of the tank is 6 times the radius of the base of the tank. Find thevolume corrected to 2 decimal places.

Answer - 8 : - Rate of painting = 50 paise per dm²
Total cost = ₹198

Question - 9 : - The radii of two cylinders are in the ratio 2 : 3 andtheir heights are in the ratio 5:3. Calculate the ratio of their volumes andthe ratio of their curved surfaces.

Answer - 9 : -

Ratio in radii of two cylinders = 2:3
and ratio in their heights = 5:3
Let radius of the first cylinder (r₁) = 2x
and radius of second cylinder (r₂) = 3x
and height of first cylinders (h₁) = 5y
and height of second cylinder (h₂) = 3y
(i) Now volume of the first cylinder = πr²h = π(2x)² x5y = 20πx²2y
and volume of tlie second cylinder = π(3x)² x 3y = π x 9×2 x 3y= 27πx²y
Now ratio in their volume
= 20πx²y : 21πx²y = 20 : 27
(ii) Curved surface area of first cylinder = 2πrh = 2π x 2x x 5y =20πxy
and curved surface area of second cylinder = 2π x 3x x = 1 8πxy
∴ Ratioin their curved surface area
= 20πxy : 18πxy = 10 : 9

Question - 10 : - The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm².

Answer - 10 : - Ratio in curved surface area and total surface area ofa cylinder =1:2
Total surface area = 616 cm²

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