## RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13B

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13B.

**Other Exercises**

- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13A
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13B
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13C
- RS Aggarwal Solutions Class 9 Chapter 13 Volume and Surface Area Ex 13D

**Question 1.**

**Find the volume and curved surface area of a right circular cylinder of height 21cm and base radius 5cm.**

**Solution:**

Radius of the base of a cylinder (r) = 5cm.

and height (h) = 21cm

**Question 2.**

**The diameter of a cylinder is 28cm and its height is 40cm. Find the curved surface area, total surface area and the volume of the cylinder.**

**Solution:**

Diameter of the base of the cylinder = 28cm

Radius = x 28 = 14 cm

Height (h) = 40cm.

**Question 3.**

**Find the weight of a solid cylinder of radius 10.5 cm end height 60cm if the material of the cylinder weighs 5g. per cm³.**

**Solution:**

Radius of cylinder (r) = 10.5cm

Height (h) = 60cm.

**Question 4.**

**The current surface area of a cylinder is 1210 cm² and its diameter is 20 cm. Find its height and volume.**

**Solution:**

Diameter of cylinder = 20cm

Radius (r) = = 10cm

**Question 5.**

**The curved surface area of a cylinder is 4400 cm², and the circumference of its base is 110 cm. Find the height and the volume of the cylinder.**

**Solution:**

Curved surface area of cylinder = 4400 cm²

Circumference of its base = 110 cm

**Question 6.**

**The radius of the base and height of a cylinder are in the ratio 2 : 3. If its volume is 1617 cm³, find the total surface area of the cylinder.**

**Solution:**

The ratio of the radius and height of a cylinder = 2:3

Volume =1617 cm³

Let radius = 2x

and height = 3x.

**Question 7.**

**The total surface area of a cylinder is 462 cm². Its curved surface area is one- third of its total surface area. Find the volume of the cylinder.**

**Solution:**

Total surface area of the cylinder = 462 cm²

Curved surface area = x 462 = 154

**Question 8.**

**The total surface area of a solid cylinder is 231 cm² and its curved surface area is of the total surface area. Find the volume of the cylinder.**

**Solution:**

Total surface area of solid

cylinder = 231 cm²

**Question 9.**

**The sum of the height and radius of the base of a solid cylinder 37m. If the total surface area of the cylinder be 1628 m² , find its volume.**

**Solution:**

Sum of radius and height = 37m.

and total surface area = 1628 m²

Let r be the radius

**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.**

**Solution:**

Total surface area = 616 cm²

Curved surface area = = 308

**Question 11.**

**1 cm³ of gold is drawn into a wire 0.1 mm in diameter. Find the length of the wire.**

**Solution:**

Volume of gold = 1 cm³

diameter of wire = 0.1 mn

**Question 12.**

**The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio.so 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces**

**Solution:**

Ratio in the radii of two cylinders = 2:3

and ratio in the heights = 5:3

If r1 and r2 and the radii and h1 and h2 are the heights, then

**Question 13.**

**A powder tin has a square base with side 12cm and height 17.5 cm. Another is cylindrical with diameter of its base 12 cm and height 17.5cm. Which has more capacity and by how much ?**

**Solution:**

Side of square = 12cm

and height = 17.5cm

**Question 14.**

**A cylindrical bucket, 28cm in diameter and 72 cm high, is full of water. The water is emptied into a rectangular tank, 66cm long and 28cm wide. Find the height of the water level in the tank.**

**Solution:**

Diameter of cylindrical bucket = 28cm

Radius (r) = = 14cm

Height (h) = 72cm.

**Question 15.**

**If 1cm³ of cast iron weighs 21g, find the weight of the cast iron pipe of length 1m with a base of 3cm in which the thickness of the metal is 1cm.**

**Solution:**

Length of pipe (l) = 1m = 100cm

diameter of pipe = 3cm.

Inner radius = cm

**Question 16.**

**A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25cm.The thickness of the metal is 8mm everywhere. Calculate the volume of the metal.**

**Solution:**

Internal diameter of cylindrical tube = 10.4 cm

Radius (r) = = 5.2cm.

**Question 17.**

**The barrel of a fountain pen, cylindrical in shape, is 7cm long and 5mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre ?**

**Solution:**

Length of barrel (h) = 7cm

Diameter = 5mm.

**Question 18.**

**A lead pencil consists of a cylinder of wood with a solid cylinder of graphite fitted into it. The diameter of the pencil is 7mm, the diameter of the graphite is 1 mm and the length of the pencil is 10cm. Calculate the weight of the whole pencil, if the specific v gravity of the wood is 0.7 g/cm³ and that of the graphite is 2.1 g/cm³.**

**Solution:**

Diameter of pencil = 7mm

.’. Radius (R) = mm = cm.

and diameter of graphite in it = 1mm

Hope given RS Aggarwal Class 9 Solutions Chapter 13 Volume and Surface Area Ex 13B are helpful to complete your math homework.

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