NCERT solution class 10 chapter 13 Surface Areas and Volumes exercise 13.4 mathematics ~ evidya

EXERCISE 13.4

Q 1, Ex 13.4 - Surface Areas And Volumes - Chapter 13 - Maths Class 10th - NCERT

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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.

Answer:

Radius (r₁) of

Radius (r₂) of

Capacity of glass = Volume of frustum of cone

Therefore, the capacity of the glass is

Q 2, Ex 13.4 - Surface Areas And Volumes - Chapter 13 - Maths Class 10th - NCERT

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.

Answer:

Perimeter of upper circular end of frustum = 18 cm
2Ï€r₁ =18

Perimeter of lower end of frustum = 6 cm
2Ï€r₂ = 6

Slant height (l) of frustum = 4 cm
CSA of frustum = Ï€ (r₁ + r₂) l

Therefore, the curved surface area of the frustum is 48 cm².

Q 3, Ex 13.4 - Surface Areas And Volumes - Chapter 13 - Maths Class 10th - NCERT

Question 3:

A fez, the cap used by the Turks, is shaped like the frustum of a cone (see the figure given below). 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 use for making it.

Answer:

Radius (r₂) at upper circular end = 4 cm
Radius (r₁) at lower circular end = 10 cm
Slant height (l) of frustum = 15 cm
Area of material used for making the fez = CSA of frustum + Area of upper circular end

= π (10 + 4) 15 + π (4)²
= π (14) 15 + 16 π

Therefore, the area of material used for making it is

Q 4, Ex 13.4 - Surface Areas And Volumes - Chapter 13 - Maths Class 10th - NCERT

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 Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm². [Take π = 3.14]

Answer:

Radius (r₁) of upper end of container = 20 cm
Radius (r₂) of lower end of container = 8 cm
Height (h) of container = 16 cm
Slant height (l) of frustum =

Capacity of container = Volume of frustum

Cost of 1 litre milk = Rs 20
Cost of 10.45 litre milk = 10.45 × 20
= Rs 209
Area of metal sheet used to make the container

= π (20 + 8) 20 + π (8)²
= 560 π + 64 π = 624 π cm²
Cost of 100 cm² metal sheet = Rs 8

Therefore, the cost of the milk which can completely fill the container is
Rs 209 and the cost of metal sheet used to make the container is Rs 156.75.

Q 5, Ex 13.4 - Surface Areas And Volumes - Chapter 13 - Maths Class 10th - NCERT

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 is drawn into a wire of diameter