RD Sharma MCQs: Surface Area and Volume of a Cuboid and Cube | Mathematics (Maths) Class 9 PDF Download

 Page 1


        
  
     
Q u e s t i o n : 5 5
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
a
10 cm
b
10
v
2
cm
c
10
v
3
cm
d
20 cm
S o l u t i o n :
The longest rod that can be fitted in the cubical vessel is its diagonal.
Side of the cube
So, the diagonal of the cube,
So, the length of the longest rod that can be fitted in the cubical box is .
Hence, the correct choice is
c.
Q u e s t i o n : 5 6
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of
the sum of the surface areas of three cubes, is
a
7 : 9
b
49 : 81
Page 2


        
  
     
Q u e s t i o n : 5 5
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
a
10 cm
b
10
v
2
cm
c
10
v
3
cm
d
20 cm
S o l u t i o n :
The longest rod that can be fitted in the cubical vessel is its diagonal.
Side of the cube
So, the diagonal of the cube,
So, the length of the longest rod that can be fitted in the cubical box is .
Hence, the correct choice is
c.
Q u e s t i o n : 5 6
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of
the sum of the surface areas of three cubes, is
a
7 : 9
b
49 : 81
c
9 : 7
d
27 : 23
S o l u t i o n :
Let, Side of each cube
So, the dimensions of the resulting cuboid are,
Length
Breadth
Height
Total surface area of the cuboid,
Sum of the surface areas of the three cubes,
Required ratio,
Thus, the required ratio is .
Hence the correct choice is
a.
Q u e s t i o n : 5 7
If the length of a diagonal of a cube is 8
v
3
cm, then its surface area is
a
512 cm
2
b
384 cm
2
c
192 cm
2
d
768 cm
2
S o l u t i o n :
Let,
Side of the cube
Page 3


        
  
     
Q u e s t i o n : 5 5
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
a
10 cm
b
10
v
2
cm
c
10
v
3
cm
d
20 cm
S o l u t i o n :
The longest rod that can be fitted in the cubical vessel is its diagonal.
Side of the cube
So, the diagonal of the cube,
So, the length of the longest rod that can be fitted in the cubical box is .
Hence, the correct choice is
c.
Q u e s t i o n : 5 6
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of
the sum of the surface areas of three cubes, is
a
7 : 9
b
49 : 81
c
9 : 7
d
27 : 23
S o l u t i o n :
Let, Side of each cube
So, the dimensions of the resulting cuboid are,
Length
Breadth
Height
Total surface area of the cuboid,
Sum of the surface areas of the three cubes,
Required ratio,
Thus, the required ratio is .
Hence the correct choice is
a.
Q u e s t i o n : 5 7
If the length of a diagonal of a cube is 8
v
3
cm, then its surface area is
a
512 cm
2
b
384 cm
2
c
192 cm
2
d
768 cm
2
S o l u t i o n :
Let,
Side of the cube
Length of the diagonal
We have to find the surface area of the cube
Surface area of the cube,
Thus, surface area of the cube is .
Hence, the correct choice is
b.
Q u e s t i o n : 5 8
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
a
8 : 1
b
2
v
2: 1
c
2 : 1
d
none of these
S o l u t i o n :
Let,
Volumes of the two cubes
Edges of the two cubes
We know that,
So,
Ratio of their edges is .
So, the correct choice is
c.
Page 4


        
  
     
Q u e s t i o n : 5 5
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
a
10 cm
b
10
v
2
cm
c
10
v
3
cm
d
20 cm
S o l u t i o n :
The longest rod that can be fitted in the cubical vessel is its diagonal.
Side of the cube
So, the diagonal of the cube,
So, the length of the longest rod that can be fitted in the cubical box is .
Hence, the correct choice is
c.
Q u e s t i o n : 5 6
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of
the sum of the surface areas of three cubes, is
a
7 : 9
b
49 : 81
c
9 : 7
d
27 : 23
S o l u t i o n :
Let, Side of each cube
So, the dimensions of the resulting cuboid are,
Length
Breadth
Height
Total surface area of the cuboid,
Sum of the surface areas of the three cubes,
Required ratio,
Thus, the required ratio is .
Hence the correct choice is
a.
Q u e s t i o n : 5 7
If the length of a diagonal of a cube is 8
v
3
cm, then its surface area is
a
512 cm
2
b
384 cm
2
c
192 cm
2
d
768 cm
2
S o l u t i o n :
Let,
Side of the cube
Length of the diagonal
We have to find the surface area of the cube
Surface area of the cube,
Thus, surface area of the cube is .
Hence, the correct choice is
b.
Q u e s t i o n : 5 8
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
a
8 : 1
b
2
v
2: 1
c
2 : 1
d
none of these
S o l u t i o n :
Let,
Volumes of the two cubes
Edges of the two cubes
We know that,
So,
Ratio of their edges is .
So, the correct choice is
c.
Q u e s t i o n : 5 9
The volume of a cube whose surface area is 96 cm
2
, is
a
16
v
2cm
3
b
32 cm
3
c
64 cm
3
d
216 cm
3
 
S o l u t i o n :
Let,
Side of the cube
Volume of the cube
Surface area of the cube
We have,
So,
Thus, volume of the cube is .
Hence the correct choice is
c.
Q u e s t i o n : 6 0
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm
3
, the
total surface area of the box is
a
27 cm
2
b
32 cm
2
c
44 cm
2
d
88 cm
2
Page 5


        
  
     
Q u e s t i o n : 5 5
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
a
10 cm
b
10
v
2
cm
c
10
v
3
cm
d
20 cm
S o l u t i o n :
The longest rod that can be fitted in the cubical vessel is its diagonal.
Side of the cube
So, the diagonal of the cube,
So, the length of the longest rod that can be fitted in the cubical box is .
Hence, the correct choice is
c.
Q u e s t i o n : 5 6
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of
the sum of the surface areas of three cubes, is
a
7 : 9
b
49 : 81
c
9 : 7
d
27 : 23
S o l u t i o n :
Let, Side of each cube
So, the dimensions of the resulting cuboid are,
Length
Breadth
Height
Total surface area of the cuboid,
Sum of the surface areas of the three cubes,
Required ratio,
Thus, the required ratio is .
Hence the correct choice is
a.
Q u e s t i o n : 5 7
If the length of a diagonal of a cube is 8
v
3
cm, then its surface area is
a
512 cm
2
b
384 cm
2
c
192 cm
2
d
768 cm
2
S o l u t i o n :
Let,
Side of the cube
Length of the diagonal
We have to find the surface area of the cube
Surface area of the cube,
Thus, surface area of the cube is .
Hence, the correct choice is
b.
Q u e s t i o n : 5 8
If the volumes of two cubes are in the ratio 8: 1, then the ratio of their edges is
a
8 : 1
b
2
v
2: 1
c
2 : 1
d
none of these
S o l u t i o n :
Let,
Volumes of the two cubes
Edges of the two cubes
We know that,
So,
Ratio of their edges is .
So, the correct choice is
c.
Q u e s t i o n : 5 9
The volume of a cube whose surface area is 96 cm
2
, is
a
16
v
2cm
3
b
32 cm
3
c
64 cm
3
d
216 cm
3
 
S o l u t i o n :
Let,
Side of the cube
Volume of the cube
Surface area of the cube
We have,
So,
Thus, volume of the cube is .
Hence the correct choice is
c.
Q u e s t i o n : 6 0
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm
3
, the
total surface area of the box is
a
27 cm
2
b
32 cm
2
c
44 cm
2
d
88 cm
2
S o l u t i o n :
Length (l), width (b) and height (h) of the rectangular solid are in the ratio 3 : 2 : 1.
So we can take,
We need to find the total surface area of the box
Volume of the box,
Thus,
Surface area of the box,
Thus total surface area of the box is .
Hence, the correct option is
d.
Q u e s t i o n : 6 1
If the areas of the adjacent faces of a rectangular block are in the ratio 2 : 3 : 4 and its volume is 9000 cm
3
, then the
length of the shortest edge is
a
30 cm
b
20 cm
c
15 cm
d
10 cm
S o l u t i o n :
Let, the edges of the cuboid be a cm, b cm and c cm.
And, a < b < c