# Gujarat Board Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.4

Gujarat Board Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.4

## Gujarat Board Textbook Solutions Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.4

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:

Here

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:

Here,

Slant height l = 4 cm

and let r_{1} r_{2} be the radii of frustum and r_{1} > r_{2
}

Perimeter of circular ends = 2πr_{1}

2πr_{1} = 18 cm

⇒ πr_{1} = 9 cm ……(1)

and 2πr_{2} = 6 cm

πr_{2} = 3 cm …….(2)

Curved surface area of frustum

= π(r_{1} + r_{2}) l = (πr_{1} + πr_{2})l ……(3)

Putting value of eqn. (1) and (2) in eqn. (3),

Curved surface area of frustum = (9 + 3) x 4 = 12 x 4 = 48 cm^{2}

Question 3.

A fez, the cap used by the Turks, is shaped like the frustum of a cone. 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:

Here

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

and r_{1} = 4 cm (Radius of the upper base)

Surface area of cap = CSA of frustum + Area of upper circular end

= π(r_{1} + r_{2}) l + πr^{2}_{2
}

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 cm^{2}. (Take π = 3.14)

Solution:

Here

h = 16 cm

r_{1} = 20 cm and r_{2} = 8 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:

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