NCERT Solution For Class 9, Maths, Chapter 13, Surface Areas And Volumes, Exercise 13.6 has questions related to cylindrical shapes in which diameter and length of any cylinder is given with which we need to find volume of the given figure. Exercise 13.6 class 9 maths chapter 13 contains total eight questions to discuss.
Class 9, Maths, Chapter 13, Exercise 13.6 Solutions (Page no. 230)
Q.1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many liters of water can it hold? (1000 cm3 = 1l)
Ans: Let r cm be the radius of the base and h cm be the height of the cylinder.
Circumference of the base = 132 cm
⇒ 2πr = 132
⇒ $2\times \frac{22}{7}\times r=132$
⇒ $r=\frac{132\times 7}{2\times 22}$= 21 cm
Volume of the cylinder = πr2h cm3
= $\frac{22}{7}\times 21\times 21\times 25$ = 34650 cm3
Vessel can hold = $\frac{34650}{1000}Liters$
i.e., 3465 liters of water.
Q.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 cm3 of wood has a mass of 0.6 g.
Ans:
Q.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?
Ans: (i) Capacity of tin can = lbh cm3
= (5 × 4 × 15) cm3 = 300 cm3
(ii) Capacity of plastic cylinder = πr2h cm3
= $\left( \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 10 \right)cm$ = 385 cm3
Thus, the plastic cylinder has greater capacity by 385 cm3
Q.4. If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find
(i) radius of its base
(ii) its volume. (Use π = 3.14)
Ans: (i) Let r be the radius of the base and h be the height of the cylinder. Then
Lateral surface = 94.2 cm3
⇒ 2 × 3.14 × r × 5 = 94.2
⇒ $r=\frac{94.2}{2\times 3.14\times 5}$= 3
Thus, the radius of its base = 3 cm
(ii) Volume of the cylinder = πr2h
= (3.14 × 32 × 5) cm3
= (3.14 x 3 x 3 x 5) cm3
= 141. 3 cm3
Q.5. It costs ₹ 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of ₹ 20 per m2, find
(i) inner curved surface area of the vessel,
(ii) radius of the base,
(iii) capacity of the vessel.
Ans:
Q.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?
Ans:
Q.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.
Ans:
Q.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?
Ans: Diameter of the cylindrical bowl = 7 cm
Radius = $\frac{7}{2}cm$
Height of serving bowl = 4 cm
Soup saved in on serving = Volume of the bowl
= πr2h
= cm3 =1.54 cm3
Soup served to 250 patient = (250×1.54) cm3
= 38500 cm3 i.e., 38.5 liters.
NCERT Solutions For Class 9, Maths, Chapter 13, Surface Areas And Volumes (All Exercises)
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.1
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.2
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.3
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.4
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.5
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.6
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.7
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.8
- Class 9, Maths, Surface Areas And Volumes, Exercise 13.9