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

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 13C.

**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, curved surface area and the total surface area of a cone having base radius 35cm and the height 84 cm.**

**Solution:**

Radius of base (r) = 35cm

and height (h) = 84cm.

**Question 2.**

**Find the volume, curved surface area and the total surface area of a cone whose height and slant height are 6cm and 10cm respectively (Take π = 3.14.)**

**Solution:**

Height of cone (h) = 6cm

Slant height (l) = 10cm.

**Question 3.**

**The volume of a right circular cone is (100 π) cm ^{3} and its height is 12cm. Find its slant height and its curved surface area.**

**Solution:**

Volume of right circular cone = (100 π) cm

^{3}

Height (h) = 12cm.

Let r be the radius of the cone

**Question 4.**

**The circumference of the base of a cone is 44cm and its slant height is 25cm. Find the volume and curved surface area of the cone.**

**Solution:**

Circumference of the base = 44cm

**Question 5.**

**A cone of slant height 25cm has a curved surface area 550 cm ^{2}. Find the height and volume of the cone.**

**Solution:**

Slant height of the cone (l) = 25cm

Curved surface area = 550 cm

^{2}

Let r be the radius

πrl = curved surface area

**Question 6.**

**Find the volume of a cone having radius of the base 35cm and slant height 37cm.**

**Solution:**

Radius.of base (r) = 35cm.

Slant height (l) = 37cm.

We know that

**Question 7.**

**The curved surface area of a cone is 4070 cm ^{2} and its diameter is 70 cm. Find its slant height.**

**Solution:**

Curved surface area = 4070 cm

^{2}

Diameter of the base = 70cm

**Question 8.**

**How many metres of cloth, 2.5m wide will be required to make a conical tent whose base radius is 7m and height 24 metres ?**

**Solution:**

Radius of the conical tent = 7m

and height = 24 m.

**Question 9.**

**A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height**

**Solution:**

Radius of the first cone (r) = 1.6 cm.

and height (h) = 3.6 cm.

**Question 10.**

**Two cones have their heights in the ratio 1 : 3 and the radii of their base in the ratio 3:1. Show that their volumes are in the ratio 3:1**

**Solution:**

Ratio in their heights =1:3

and ratio in their radii = 3:1

Let h1,h2 he their height and r1,r2 be their radii, then

The ratio between their volumes is 3:1

hence proved

**Question 11.**

**A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of the canvas 5m wide to make the required tent ?**

**Solution:**

Diameter of the tent = 105m

**Question 12.**

**A conical tent is to accommodate 11 persons. Each person must have 4m ^{2} of the space on the ground and 20m^{3} of air to breath. Find the height of the cone**

**Solution:**

No. of persons to be s accommodated =11

Area to be required for each person = 4m

^{2}

**Question 13.**

**A cylindrical bucket 32 cm high and 18cm of radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24cm, find the radius and the slant height of the heap.**

**Solution:**

Height of the cylindrical bucket (h) = 32cm

Radius (r) = 18cm

Volume of sand filled in it = πr^{2}h

= π x 18 x 18 x 32 cm^{3}

= 10368π cm^{3}

Volume of conical sand = 10368 π cm^{3}

Height of cone = 24 cm

**Question 14.**

**A cylinder and a cone are equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8:5, show that the radius and height of each has the ratio 3 : 4.**

**Solution:**

Let h be the height and r be the radius of the cylinder and cone.

Curved surface area of cylinder = 2πrh

and curved surface area of cone = πrl

**Question 15.**

**An iron pillar consists of a cylindrical portion 2.8 m high and 20cm in diameter and a cone 42cm high is surmounting it. Find the weight of the pillar, given that 1 cm ^{3} of iron weighs 7.5 g.**

**Solution:**

Diameter of the pillar = 20cm

Radius (r) = = 10cm

**Question 16.**

**The height of a cone is 30cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be of the volume of the given cone, at what height above the base, the section has been made?**

**Solution:**

Height of the bigger cone (H) = 30cm

By cutting a small cone from it, then volume of smaller cone = of volume of big cone

Let radius and height of the smaller cone be r and h

and radius and height of the bigger cone be R and H.

Hence at the height of 20cm from the base it was cut off. Ans.

**Question 17.**

**From a solid right circular cylinder with height 10cm and radius of the base 6cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid. (Take π = 3.14).**

**Solution:**

Height of the cylinder (h) = 10cm.

Radius (r) = 6cm.

Height of the cone = 10cm

**Question 18.**

**Water flows at the rate of 10 metres per minute through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface 40cm and depth 24cm ?**

**Solution:**

Diameter of conical vessel = 40cm

Radius (r) = = 20cm

and depth (h) = 24cm.

.’. Volume = πr^{2}h

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

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