Find the curved surface of a cylinder, whose radius of base is 7 cm and height 10 cm.
2. Find the total surface area and the volume of a cylindrical container, whose diameter of base is 14 cm and
which is 15 cm long.
3. How much water can a cylindrical container hold, if its radius of base is 3.5 cm and it is 6 cm long?
4. Find the cost of painting the curved surface of a cylinder of base diameter 35 cm and height 20 cm at the rate of 20 paise per cm2.
5. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same? (NCERT)
6. A cylindrical bucket is 28 cm high and its radius of base is 12 cm. Find the amount of water (in litres) it can hold. (1000 cm3= 1 l)
7. Savitri had to make a model of a cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25 cm with a 3.5 cm radius?
Take π =22/7 (NCERT)
8. The pillars of a temple are cylindrically shaped (see Fig.). 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)
9. 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? (NCERT)
10. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. (NCERT)
11. Find height of a right circular cylinder whose radius of base is 10 cm and area of curved surface is 880 cm2.
12. If the lateral surface of a cylinder is 94.2 cm2and its height is 5 cm, then find: (NCERT)
(i) radius of its base (ii) its volume. (Use π = 3.14)
13. 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? (NCERT)
14. Find height of a right circular cylinder, whose radius of base is 10 cm and volume is 4400 cm3.
Answers
Question 1) :- Find the curved surface of a cylinder, whose radius of base is 7 cm and height 10 cm. ?
Answer :-
we know that,
- CSA of cylinder = 2 * π * radius * height .
putting given values we get,
→ CSA of cylinder = 2 * (22/7) * 7 * 10 = 44 * 10 = 440 cm² (Ans.)
Question 2) :- Find the total surface area and the volume of a cylindrical container, whose diameter of base is 14 cm and which is 15 cm long.
we know that,
- TSA of cylinder = 2πr(h + r)
- Volume of cylinder = π * r² * h .
- radius = Diameter/2
putting given values we get,
→ TSA = 2 * (22/7) * 7 * (15 + 7)
→ TSA = 2 * 22 * 22
→ TSA = 968 cm². (Ans.)
and,
→ Volume = (22/7) * 7 * 7 * 15
→ Volume = 22 * 7 * 15
→ Volume = 2310 cm³. (Ans.)
Question 3) :- How much water can a cylindrical container hold, if its radius of base is 3.5 cm and it is 6 cm long ?
Solution :-
→ Volume of cylinder = π * r² * h
→ Volume = (22/7) * (3.5) * (3.5) * 6
→ Volume = 22 * 0.5 * 3.5 * 6
→ Volume = 231 cm³.
now, we know that,
- 1000 cm³ = 1 litre .
therefore,
→ 231 cm³ = (231/1000) = 0.231 Litre (Ans.)
Question 4) :- Find the cost of painting the curved surface of a cylinder of base diameter 35 cm and height 20 cm at the rate of 20 paise per cm².
Answer :-
→ CSA of cylinder = 2 * π * r * h
→ CSA = 2 * (22/7) * (35/2) * 20
→ CSA = 22 * 5 * 20
→ CSA = 2200 cm².
then,
→ Total cost of Painting = Rate / m² * CSA = 20 paise * 2200 = 0.2 * 2200 = Rs.440 (Ans.)
Question 5) :- It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same ? (NCERT)
Solution :-
→ CSA of cylinder = Area of metal sheet .
→ CSA = 2 * (22/7) * (70/100) * 1
→ CSA = 2 * 22 * (1/10)
→ CSA = 4.4 m² (Ans.)
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