## Chapter 13 Surface Areas and Volumes Ex 13.4

**Unless stated otherwise, take π = **22/7

**Question 1.**

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular .ends are 4 cm and 2 cm. Find the capacity of the glass.
**Solution:**

**Question 2.**

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
**Solution:**

Given: upper circumference of the frustum = 18 cm

Slant height (l) = 4 cm

We have C.S.A of the frustum = π (r_{1} + r_{2})l

Putting values from equation (i) and (ii), we get

Curved surface area = (πr_{1} + πr_{2})l = (9 + 3) x 4 = 12 x 4 = 48 cm²

**Question 3.**

A fez, the cap used by the Turks, is shaped like the frustum of a cone (see figure). If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

**Solution:**

Radius of open side (r_{1}) = 10 cm

Radius of upper base (r_{2}) = 4 cm

Slant height (l) = 15 cm

Total surface area of the cap = C.S.A. of the frustum + Area of upper base

= 660 cm² + 50.28 cm² = 710.28 cm²

**Question 4.**

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of ₹ 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 8 per 100 cm2. (Take π = 3.14)
**Solution:**

Radius of the lower end (r_{1}) = 8 cm

Radius of the upper end (r_{2}) = 20 cm

Height of the frustum (h) = 16 cm

**Question 5.**

A metallic right circular cone 20 cm high and whose vertical angle is 60° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16 cm, find the length of the wire.
**Solution:**

Let ADC is a cone with vertical angle 600.

Now, cone is cut into two parts, parallel to its base at height 10 cm.

Radius of larger end of the frustum = R_{1}

A wire be formed having diameter 1/16 cm and length be H cm

Volume of wire so obtained = πr²H