RBSE Solutions for Class 9 Maths Chapter 12 Surface Area and Volume of Cube and Cuboid Miscellaneous Exercise

RBSE Solutions for Class 9 Maths Chapter 12 Surface Area and Volume of Cube and Cuboid Miscellaneous Exercise is part of RBSE Solutions for Class 9 Maths. Here we have given Rajasthan Board RBSE Class 9 Maths Solutions Chapter 12 Surface Area and Volume of Cube and Cuboid Miscellaneous Exercise.

BoardRBSE
TextbookSIERT, Rajasthan
ClassClass 9
SubjectMaths
ChapterChapter 12
Chapter NameSurface Area and Volume of Cube and Cuboid
ExerciseMiscellaneous Exercise
Number of Questions Solved14
CategoryRBSE Solutions

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 12 Surface Area and Volume of Cube and Cuboid Miscellaneous Exercise

Multiple Choice Questions

Question 1.
The volume of (RBSESolutions.com) a cube is 125 cubic metres, its side is:
(A) 7 m
(B) 6 m
(C) 5 m
(D) 2 m
Solution.
(C) 5 m

Question 2.
The volume of a cube is 1331 cubic centimetre, then it surface area is:
(A) 762 sq. cm
(B) 726 sq. cm
(C) 426 sq. cm
(D) 468 sq. cm
Solution.
(B) 726 sq. cm

RBSE Solutions

Question 3.
The length, breadth and height of (RBSESolutions.com) a cuboid are 4 m, 3 m and 2 m respectively, then surface area of cuboid:
(A) 25 sq. m
(B) 26 sq. m
(C) 52 sq. m
(D) 62 sq. m
Solution.
(C) 52 sq. m

Question 4.
The diagonal of a cuboid having dimension 8mx7mx6mis:
(A) 12.2 m
(B) 12.02 m
(C) 14.2 m
(D) 14.02 m
Solution.
(A) 12.2 m

Question 5.
The edge of (RBSESolutions.com) a cube is 5 cm, its diagonal
will be:
(A) 4√3cm
(B) 2√3 cm
(C) 5√3 cm
(D) 5 cm
Solution.
(C) 5√3 cm

Question 6.
The volume of cuboid is 400 cubic centimetre, and area of its (RBSESolutions.com) base is 80 sq. cm, then its height is:
(A) 7 cm
(B) 6 cm
(C) 4 cm
(D) 5 cm
Solution.
(D) 5 cm

Question 7.
A cuboid measuring 15 cm x 12 cm x 6 cm is melted. How many (RBSESolutions.com) new cubes of sides 3 cm can be made?
Solution.
Required number of new cubes
RBSE Solutions for Class 9 Maths Chapter 12 Surface Area and Volume of Cube and Cuboid Miscellaneous Exercise

Question 8.
Two cubical dice having edge 2 cm are (RBSESolutions.com) joined end to end. Find the total surface area of the solid so formed.
Solution.
Length of the solid = 2 + 2 = 4 cm
Breadth = 2 cm
Height = 2 cm
Surface area = 2(lb + bh + hl)
= 2(4 x 2 + 2 x 2 + 2 x 4)
= 2(8 + 4 + 8)
= 2 x 20
= 40 cm

RBSE Solutions

Question 9.
An empty tank is 4 m long and 3 m wide. How many cubic metre of (RBSESolutions.com) water must be filled in .it so that depth of water become 2 m?
Solution.
Length = 4 m, Breadth = 3 m and depth = 2 m
Volume of empty tank = l x b x h = (4 x 3 x 2) m3 = 24 m3
Hence, 24 m3 of water must be filled in the empty tank so that depth of water in the tank becomes 2 m.

Question 10.
A cubical vessel contains 8 litres of water. Find the total surface area of the vessel.
Solution.
Here, volume of vessel = 8 litres
But 1 litre = 1000 cm3
8 litres = 8000 cm3
Let the side of the cubical vessel be l, therefore we can write
Volume = l3
⇒ l3 = 8000
⇒ l3 = (20)3
⇒ l = 20 cm
Now, total surface area is 6l2
Area = 6 x (20)2 = 6 x 400 = 2400
Hence, total surface area = 2400 cm3

Question 11.
A godown measures 60 m x 25 m x 10 m. Find the maximum number (RBSESolutions.com) of wooden crates each measuring 1.5 m x 1.25 m x 0.5 m that can be stored in the godown.
Solution.
We have,
Length of godown = 60 m
Breadth = 25 m and height = 10 m
Volume/capacity of the godown = (60 x 25 x 10) m3
Volume of one wooden crate = (1.5 x 1.25 x 0.5) m3
Required number of wooden crates
RBSE Solutions for Class 9 Maths Chapter 12 Surface Area and Volume of Cube and Cuboid Miscellaneous Exercise
Hence, maximum 16000 crates can be stored in the godown.

Question 12.
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much (RBSESolutions.com) water will fall into the sea in a minute?
Solution.
Water flowed in one minute = \(\frac { 2×1000 }{ 60 }\) = \(\frac { 100 }{ 3 }\) m
Volume of water fell into the sea in one minute
= \(\frac { 100 }{ 3 }\) x 40 x 3 = 4000 m3

Question 13.
The dimension of rectangular parallelopiped are in the ratio 6 : 5 : 4 and its total surface area is 33300 square metres. Find its volume.
Solution.
Let length, breadth and height of a cuboid are 6x, 5x and 4x respectively.
Its total surface area
= 2(lb + bh + hl)
= 2(6x × 5x + 5x × 4x + 4x × 6x)
= 2(30 x 2 + 20 x 2 + 24 x 2)
= 2 x 74 x 2
= 148 x 2
But it is given that total (RBSESolutions.com) surface area = 333000 sq.m
i.e. 148 x 2 = 33300
⇒ x2 = \(\frac { 33300 }{ 148 }\)
⇒ x2 = 225 m2
⇒ x = √225
⇒ x = 15 m
Dimensions of cuboid are
6x = 6 × 15 = 90 m
5x = 5 × 15 = 75 m
and 4x = 4 × 15 = 60 m
Volume of cuboid = 90 × 75 × 60 cubic metres = 405000 cubic metres.

RBSE Solutions

Question 14.
A field is 20 metres long and 15 metres wide. A pit (outside the field) 10 metres long and 6 metres wide is due to a depth of 5 m and the earth is spread uniformly in the field. By (RBSESolutions.com) how much the level of field is raised?
Solution.
Dimension of the field are 20 m and 15 m respectively
i.e. length of the field = 20 m
and breadth of the field = 15 m
Now volume of the earth taken out from the pit = l × b × h = 10 × 6 × 5 = 300 cubic metres
Due to 300 cubic metre of earth, suppose the level of field be raised by h metres.
Volume of the field = Volume of earth taken out from the pit
⇒ 20 x 15 x h = 300
⇒ h = \(\frac { 300 }{ 300 }\) = 1 m
Hence, level of the field be raised by 1 m.

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