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NCERT Exemplar · Class 9 · Maths

Chapter 13: Surface Areas and Volumes

Practice each question, then open the answer or worked solution.

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Exercise 13.4

Textbook page 127 · 4 questions
Q1Written answer

A cylindrical tube opened at both the ends is made of iron sheet which is 2 cm thick. If the outer diameter is 16 cm and its length is 100 cm, find how many cubic centimeters of iron has been used in making the tube?

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Worked solution

According to the question,

Outer diameter d = 16cm

Then,

Outer radius r – 16/2 = 8cm

Height = length = 100cm

Thickness of iron sheet = 2cm

Volume of cylinder = πr2h, where r= outer radius and π = 3.14

Thus, Volume of cylinder = πr2h

= 3.14 × (8)2× 100

= 20,096 cm3

Now, inner diameter = outer diameter – 2× thickness of iron sheet

Inner diameter = 16-(2× 2) = 12cm

Inner radius R = 12/2 = 6cm

Thus, Volume of hollow space = πR2 h, where R= inner radius and π = 3.14

= πR2 h

= 3.14 × (6)2× 100

= 11,304 cm3

Thus,

Volume of iron used = Volume of cylinder – Volume of hollow space

= (20,096 – 11,304 ) cm3

= 8800 cm3

Q2Written answer

A semi-circular sheet of metal of diameter 28cm is bent to form an open conical cup. Find the capacity of the cup.

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Worked solution

According to the question,

Diameter of semi circular sheet = 28cm

Radius of semi circular sheet (r) = 28/2

= 14cm

Semi Circular sheet is bent to form an open conical cup

Thus, slant height of a conical cup (l)=radius of semicircular sheet(r) = 14cm

We know that,

Circumference of base of a cone = 2πR,

(where, R = radius of a cone and circumference of semi circle = πr)

Thus,

Circumference of base of a cone = Circumference of a Semi circle

⇒ 2πR= πr

NCERT Exemplar Solutions Class 9 Maths Chapter 13- Ex.13.4-1

To find height,

R2 + h2 = l2

Where,

R=radius of a cone

h=height of a cone

l=slant height of a cone

⇒ (7)2 + h2 = (14)2

⇒ 49+ h2 = 196

⇒ h2 = 196 – 49 = 147

⇒ h = √147 = 7√3 cm

Thus, volume of a cone = 1/3 πR2h
NCERT Exemplar Solutions Class 9 Maths Chapter 13- Ex.13.4-2

Q3Written answer

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m

(i) How many students can sit in the tent if a student, on an average, occupies 5/7 m2 on the ground?

(ii) Find the volume of the cone.

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Worked solution

According to the question,

Area of cloth = 165m2

Radius of conical tent = 5m

Area covered by 1 student = 5/7 m2

Curved surface area of cone = πrl

Thus, curved surface area of a conical; tent =  πrl

NCERT Exemplar Solutions Class 9 Maths Chapter 13- Ex.13.4-3

(i)

NCERT Exemplar Solutions Class 9 Maths Chapter 13- Ex.13.4-4

(ii) Height of a cone,

r2 + h2 = l2

Where,

r=radius of a cone

h=height of a cone

l=slant height of a cone

⇒ (5)2 + h2 = (10.5)2

⇒ 25+ h2 = 110.25

⇒ h2 = 110.25 – 25 = 85.25

⇒ h = √85.25 = 9.23 m

Volume of a come = (1/3) πr2h

NCERT Exemplar Solutions Class 9 Maths Chapter 13- Ex.13.4-5

Q4Written answer

The water for a factory is stored in a hemispherical tank whose internal diameter is 14 m. The tank contains 50 kilolitres of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

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Worked solution

According to the question,

Internal diameter of hemispherical tank = 14 m

Internal radius of hemispherical tank = 14/2 m = 7m

Tank contains 50kl = 50m3 of water (since, 1kl = 1m3)

Volume of a hemispherical tank = 2/3 πr3
NCERT Exemplar Solutions Class 9 Maths Chapter 13- Ex.13.4-6

Volume of water pumped into the tank = Volume of hemispherical tank – 50m3

= 718.66 – 50

= 668.66 m3