NCERT Solutions for Class 10 Maths Exercise 13.4 Chapter 13 Surface Areas and Volumes- FREE PDF Download

NCERT Class 10 Maths Ch 13 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths
Chapter 13 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Surface Areas and Volumes solutions will help you understand the chapter thoroughly.

NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes

Unless stated otherwise, take

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.

Ans. Here, = 2 cm,

= 1 cm and = 14 cm

Capacity of the glass =

= $\frac{308}{3} = 102 \frac{2}{3} c m^{3}$

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.

Ans. Let cm and cm be the radii of the ends of the frustum of the cone.

Then, = 4 cm

= 18 cm

= 9 cm

= 6 cm

= 3 cm

Now, CSA of the frustum =

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.

Ans.

Here, = 10 cm,

= 4 cm and = 15 cm

Surface area =

= =

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 total cost of milk which can completely fill the container at the rate of Rs. 20 per liter. Also find the cost of metal sheet used to make the container, if it costs Rs. 8 per 100 cm².

Ans. Here, = 20 cm,

= 8 cm and = 16 cm

Volume of container =

= $\frac{1}{3} \times 3.14 \times 16 {{(20)}^{2} + {(8)}^{2} + 20 \times 8}$

= = 10.44992 liters

Cost of the milk =

= Rs. 208.9984 = Rs. 209

Now, surface area = +

= +

= 1758.4 + 200.96

Area of the metal sheet used =

Cost of metal sheet =

= 156.7488 = Rs. 156.75

5. A metallic right circular cone 20 cm high and whose vertical angle is 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 cm, find the length of the wire.