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# 07 - Question bank -Surface Area and Volume - Class 10 - Maths Class 10 Notes | EduRev

## Class 10 : 07 - Question bank -Surface Area and Volume - Class 10 - Maths Class 10 Notes | EduRev

``` Page 1

Surface and volume of cube, cuboid, and cylinder

Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m.
Given: For Cuboidal Room,
Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m
To find  cost of painting four walls we first need to find the surface area of four walls .
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h

Vertical surface area of cuboid=180 m
2
.
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting
=180×13
=2340
Therefore Cost of Painting the four wall is 2340 Rs

Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what
will be the weight of the pillar.
Given: For Pillar [cuboid]
Length =600cm=
600
100
=6m
55
100
=0.55m
Height=25cm=
25
100
=0.25m

=2(10+5)×6
=2(15)×6
=180

l
h
b
Tip: Remember to convert
dimensions from cm to m as
weight per cube is given in m
3
Page 2

Surface and volume of cube, cuboid, and cylinder

Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m.
Given: For Cuboidal Room,
Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m
To find  cost of painting four walls we first need to find the surface area of four walls .
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h

Vertical surface area of cuboid=180 m
2
.
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting
=180×13
=2340
Therefore Cost of Painting the four wall is 2340 Rs

Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what
will be the weight of the pillar.
Given: For Pillar [cuboid]
Length =600cm=
600
100
=6m
55
100
=0.55m
Height=25cm=
25
100
=0.25m

=2(10+5)×6
=2(15)×6
=180

l
h
b
Tip: Remember to convert
dimensions from cm to m as
weight per cube is given in m
3
Solution
Volume of Beam pillar[cuboid]= ?? × ?? × h
=6×0.55×0.25
=0.825 m
3

Weight of pillar=Volume of pillar×weight of volume per m
3

=0.825×200
=165 Kg
Weight of pillar=165 Kg

Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a
playground. Find the area of playground in m
2
.
Solution: The Diameter cylindrical roller =40 cm
40
2
= 20 cm
Length of cylindrical roller (h) =140 cm
Curved surface area of cylindrical roller = 2 ???? h
=2 ×
2 2
7
× 20 × 140
=17600 cm
2
=17600/10000    =1.76 m
2

Area covered in one revolution is = curved surface area of cylinder
= 1.76 m
2

Total Area of Playground= No. of revolutions × curved surface area of cylinder
= 350×1.76
=616 m
2

Area of Playground= 616 m
2
.

Tip: Since the shape of
roller is like cylinder, we
will use formula for
cylinder.

Note: Since we are
converting cm
2
to m
2
we
need to divide it by
100×100
Page 3

Surface and volume of cube, cuboid, and cylinder

Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m.
Given: For Cuboidal Room,
Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m
To find  cost of painting four walls we first need to find the surface area of four walls .
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h

Vertical surface area of cuboid=180 m
2
.
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting
=180×13
=2340
Therefore Cost of Painting the four wall is 2340 Rs

Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what
will be the weight of the pillar.
Given: For Pillar [cuboid]
Length =600cm=
600
100
=6m
55
100
=0.55m
Height=25cm=
25
100
=0.25m

=2(10+5)×6
=2(15)×6
=180

l
h
b
Tip: Remember to convert
dimensions from cm to m as
weight per cube is given in m
3
Solution
Volume of Beam pillar[cuboid]= ?? × ?? × h
=6×0.55×0.25
=0.825 m
3

Weight of pillar=Volume of pillar×weight of volume per m
3

=0.825×200
=165 Kg
Weight of pillar=165 Kg

Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a
playground. Find the area of playground in m
2
.
Solution: The Diameter cylindrical roller =40 cm
40
2
= 20 cm
Length of cylindrical roller (h) =140 cm
Curved surface area of cylindrical roller = 2 ???? h
=2 ×
2 2
7
× 20 × 140
=17600 cm
2
=17600/10000    =1.76 m
2

Area covered in one revolution is = curved surface area of cylinder
= 1.76 m
2

Total Area of Playground= No. of revolutions × curved surface area of cylinder
= 350×1.76
=616 m
2

Area of Playground= 616 m
2
.

Tip: Since the shape of
roller is like cylinder, we
will use formula for
cylinder.

Note: Since we are
converting cm
2
to m
2
we
need to divide it by
100×100
Q.4) The curved surface area of cylinder is 154 cm
2
. The total surface area of the cylinder is
thrice the curved surface area. Find the volume of cylinder.[ p=22/7]
Given: curved surface area of cylinder (2 ???? h )= 154 cm
2
Solution

Curved surface area of cylinder ( ???? ?? ?? )= 154 cm
2

?? ×
????
?? × ?? × ?? = ??????
h=
??????
?? × ????

h= ?? . ??   cm
Volume of Cylinder= ?? ?? ?? ??
=
????
?? × ?? × ?? × ?? . ??
= 539 cm
3
Volume of Cylinder= 539 cm
3

:

Total surface area of cylinder= 2 ×curved surface area

2 ???? h + 2 ?? ?? 2
= 3 × 154
154 +2 pr
2
= 462
2 pr
2
=462– 154
2 pr
2
=308
2 ×
2 2
7
× ?? 2
= 308
r
2
=
3 0 8 × 7
2× 2 2

r
2
=49
r=7

Page 4

Surface and volume of cube, cuboid, and cylinder

Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m.
Given: For Cuboidal Room,
Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m
To find  cost of painting four walls we first need to find the surface area of four walls .
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h

Vertical surface area of cuboid=180 m
2
.
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting
=180×13
=2340
Therefore Cost of Painting the four wall is 2340 Rs

Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what
will be the weight of the pillar.
Given: For Pillar [cuboid]
Length =600cm=
600
100
=6m
55
100
=0.55m
Height=25cm=
25
100
=0.25m

=2(10+5)×6
=2(15)×6
=180

l
h
b
Tip: Remember to convert
dimensions from cm to m as
weight per cube is given in m
3
Solution
Volume of Beam pillar[cuboid]= ?? × ?? × h
=6×0.55×0.25
=0.825 m
3

Weight of pillar=Volume of pillar×weight of volume per m
3

=0.825×200
=165 Kg
Weight of pillar=165 Kg

Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a
playground. Find the area of playground in m
2
.
Solution: The Diameter cylindrical roller =40 cm
40
2
= 20 cm
Length of cylindrical roller (h) =140 cm
Curved surface area of cylindrical roller = 2 ???? h
=2 ×
2 2
7
× 20 × 140
=17600 cm
2
=17600/10000    =1.76 m
2

Area covered in one revolution is = curved surface area of cylinder
= 1.76 m
2

Total Area of Playground= No. of revolutions × curved surface area of cylinder
= 350×1.76
=616 m
2

Area of Playground= 616 m
2
.

Tip: Since the shape of
roller is like cylinder, we
will use formula for
cylinder.

Note: Since we are
converting cm
2
to m
2
we
need to divide it by
100×100
Q.4) The curved surface area of cylinder is 154 cm
2
. The total surface area of the cylinder is
thrice the curved surface area. Find the volume of cylinder.[ p=22/7]
Given: curved surface area of cylinder (2 ???? h )= 154 cm
2
Solution

Curved surface area of cylinder ( ???? ?? ?? )= 154 cm
2

?? ×
????
?? × ?? × ?? = ??????
h=
??????
?? × ????

h= ?? . ??   cm
Volume of Cylinder= ?? ?? ?? ??
=
????
?? × ?? × ?? × ?? . ??
= 539 cm
3
Volume of Cylinder= 539 cm
3

:

Total surface area of cylinder= 2 ×curved surface area

2 ???? h + 2 ?? ?? 2
= 3 × 154
154 +2 pr
2
= 462
2 pr
2
=462– 154
2 pr
2
=308
2 ×
2 2
7
× ?? 2
= 308
r
2
=
3 0 8 × 7
2× 2 2

r
2
=49
r=7

Surface area and volume of Cone and Frustrum

Q.1) The height of cone is 4 cm and radius is 3 cm. what will be its Total surface area
and volume?
Given: Radius of cone(r) = 3 cm
Height of cone(h) = 4 cm
Solution:
First we will find slant height of cone (l) = v h
2
+ ?? 2

l = v4
2
+ 3
2

l = v16 + 9
l = v25
l = 5 cm
Total Surface Area of Cone = ???? ( ?? + ?? )
=
2 2
7
× 3 × (3 + 5)
=
2 2
7
× 3 × 8
= 75.428 cm
2
Volume of cone =
1
3
?? ?? 2
h
=
1
3
×
2 2
7
× 3
2
× 4
=
22×3×4
7

=37.714 cm
3

Page 5

Surface and volume of cube, cuboid, and cylinder

Q.1)Find the Total cost of painting the four walls of cuboidal room at the rate of  13 Rs per
m
2
.The Dimension of the Cuboidal room are of length 10m , breadth 5m and height 6m.
Given: For Cuboidal Room,
Rate of Painting= 13 Rs/m
2
, l=10m , b=5m , h=6m
To find  cost of painting four walls we first need to find the surface area of four walls .
Solution: Vertical surface area of cuboid (four walls)=2(l+b)×h

Vertical surface area of cuboid=180 m
2
.
Total cost of painting four walls =Vertical surface area of cuboid × Rate of painting
=180×13
=2340
Therefore Cost of Painting the four wall is 2340 Rs

Q.2)A pillar of dimension 600cm×55cm×25cm made of wood which weights 200kg/m
3
.what
will be the weight of the pillar.
Given: For Pillar [cuboid]
Length =600cm=
600
100
=6m
55
100
=0.55m
Height=25cm=
25
100
=0.25m

=2(10+5)×6
=2(15)×6
=180

l
h
b
Tip: Remember to convert
dimensions from cm to m as
weight per cube is given in m
3
Solution
Volume of Beam pillar[cuboid]= ?? × ?? × h
=6×0.55×0.25
=0.825 m
3

Weight of pillar=Volume of pillar×weight of volume per m
3

=0.825×200
=165 Kg
Weight of pillar=165 Kg

Q.3)If the Diameter of roller is 40 cm and length is 140 cm. It takes 350 revolutions to land a
playground. Find the area of playground in m
2
.
Solution: The Diameter cylindrical roller =40 cm
40
2
= 20 cm
Length of cylindrical roller (h) =140 cm
Curved surface area of cylindrical roller = 2 ???? h
=2 ×
2 2
7
× 20 × 140
=17600 cm
2
=17600/10000    =1.76 m
2

Area covered in one revolution is = curved surface area of cylinder
= 1.76 m
2

Total Area of Playground= No. of revolutions × curved surface area of cylinder
= 350×1.76
=616 m
2

Area of Playground= 616 m
2
.

Tip: Since the shape of
roller is like cylinder, we
will use formula for
cylinder.

Note: Since we are
converting cm
2
to m
2
we
need to divide it by
100×100
Q.4) The curved surface area of cylinder is 154 cm
2
. The total surface area of the cylinder is
thrice the curved surface area. Find the volume of cylinder.[ p=22/7]
Given: curved surface area of cylinder (2 ???? h )= 154 cm
2
Solution

Curved surface area of cylinder ( ???? ?? ?? )= 154 cm
2

?? ×
????
?? × ?? × ?? = ??????
h=
??????
?? × ????

h= ?? . ??   cm
Volume of Cylinder= ?? ?? ?? ??
=
????
?? × ?? × ?? × ?? . ??
= 539 cm
3
Volume of Cylinder= 539 cm
3

:

Total surface area of cylinder= 2 ×curved surface area

2 ???? h + 2 ?? ?? 2
= 3 × 154
154 +2 pr
2
= 462
2 pr
2
=462– 154
2 pr
2
=308
2 ×
2 2
7
× ?? 2
= 308
r
2
=
3 0 8 × 7
2× 2 2

r
2
=49
r=7

Surface area and volume of Cone and Frustrum

Q.1) The height of cone is 4 cm and radius is 3 cm. what will be its Total surface area
and volume?
Given: Radius of cone(r) = 3 cm
Height of cone(h) = 4 cm
Solution:
First we will find slant height of cone (l) = v h
2
+ ?? 2

l = v4
2
+ 3
2

l = v16 + 9
l = v25
l = 5 cm
Total Surface Area of Cone = ???? ( ?? + ?? )
=
2 2
7
× 3 × (3 + 5)
=
2 2
7
× 3 × 8
= 75.428 cm
2
Volume of cone =
1
3
?? ?? 2
h
=
1
3
×
2 2
7
× 3
2
× 4
=
22×3×4
7

=37.714 cm
3

Q.2) The volume of the cone is 352 cm
3
and its height is 21 cm what will be the radius of
cone?
Given: volume of cone (v)= 352 cm
3

Height of cone = 21 cm
Solution
Volume of cone (v) =
1
3
?? ?? 2
h
352=
1
3
×
2 2
7
× ?? 2
× 21

3 5 2
2 2
= ?? 2

16 = ?? 2

? ?? = 4    ( ?? ?? ???? ???? ?????? ?? ???? ?????? h ???? ???? )
Ans: The radius of cone is 4 cm.

Q.3)The height of frustum is 4 cm and it’s radii are 6 cm and 3 cm. Find  curved surface
area and volume of frustum.
Given: Height of frustum (h) = 4 cm
1
) = 6 cm
2
) =3 cm
Solution:
Slant Height of the Frustum (l) = ? h
2
+ ( ?? 1
- ?? 2)
2

l = ?4
2
+ (6 - 3)
2

l = v16 + 9
l = v25
l =5 cm
Curved surface area of frustum = ?? ( ?? 1
+ ?? 2
) ??
```
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## Crash Course for Class 10 Maths by Let`s tute

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