## Chapter 13 Surface Areas and Volumes Ex 13.7

**Question 1.**
**Find the volume of the right circular cone with**
**(i) radius 6 cm, height 7 cm**
**(ii) radius 3.5 cm, height 12 cm**
**Solution:**

(i) We have, r = 6 cm and h = 7cm

**Question 2.**
**Find the capacity in litres of a conical vessel with**
**(i) radius 7 cm, slant height 25 cm**
**(ii) height 12 cm, slant height 13 cm**
**Solution:**

(i) We have, r = 7 cm and l = 25 cm

**Question 3.**
**The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use π = 3.14)**
**Solution:**

**Question 4.**
**If the volume of a right circular cone of height 9 cm is 48 cm3, find the diameter of its base.**
**Solution:**

We have, volume of a right circular cone = 48 π cm3

**Question 5.**
**A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?**
**Solution:**

We have, diameter = 3.5 m

**Question 6.**
**The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28 cm, find**
**(i) height of the cone**
**(ii) slant height of the cone**
**(iii) curved surface area of the cone**
**Solution:**

We have, d = 28cm

⇒ r = 14 cm

∵ Volume of a right circular cone = 9856 cm^{3}

**Question 7.** **A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.** **Solution:**

On revolving the right ∆ ABC about the side AB, we get a cone as shown in the adjoining figure.

**Question 8.**
**If the triangle ABC in the Question 7 above is revolved about the side 5 cm, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.**
**Solution:**

On revolving the right ∆ ABC about the side BC( = 5 cm),

we get a cone as shown in the adjoining figure.

In above Question 7, the volume V_{2} obtained by revolving the ∆ ABC about the side 12 cm i.e., V_{2} = 100π cm^{3}.

Hence, the required ratio =5:12

**Question 9.**
**A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.**
**Solution:**