Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RD Sharma (Very Short Answer Questions): Surface Area and Volume of a Cuboid and Cube
Class 9 Maths Question Answers - Surface Area and Volume of a Cuboid and Cube
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Page 1
Q u e s t i o n : 4 8
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
S o l u t i o n :
We have,
Side of each cube (a) = 6 cm
We need to find the volume of resulting cuboid
Hence, dimensions of the resulting cuboid are,
Length (l) = 2a
Page 2
Q u e s t i o n : 4 8
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
S o l u t i o n :
We have,
Side of each cube (a) = 6 cm
We need to find the volume of resulting cuboid
Hence, dimensions of the resulting cuboid are,
Length (l) = 2a
Breadth (b) = a
= 6 cm
Height (h) = a
= 6 cm
Hence, volume of the resulting cuboid,
Hence, volume of the resulting cuboid is .
Q u e s t i o n : 4 9
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is
12
v
3
cm. Find the edges of three cubes.
S o l u t i o n :
The edges of the three cubes are in the ratio 3 : 4 : 5.
So, let the edges be 3x cm, 4x cm, 5x cm.
The diagonal of new cube is
We need to find the edges of three cubes
Here, volume of the resulting cube,
Let,
Edge of the resulting cube
So, diagonal of the cube , so
Hence,
Now;
The edges of the three cubes are,
Page 3
Q u e s t i o n : 4 8
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
S o l u t i o n :
We have,
Side of each cube (a) = 6 cm
We need to find the volume of resulting cuboid
Hence, dimensions of the resulting cuboid are,
Length (l) = 2a
Breadth (b) = a
= 6 cm
Height (h) = a
= 6 cm
Hence, volume of the resulting cuboid,
Hence, volume of the resulting cuboid is .
Q u e s t i o n : 4 9
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is
12
v
3
cm. Find the edges of three cubes.
S o l u t i o n :
The edges of the three cubes are in the ratio 3 : 4 : 5.
So, let the edges be 3x cm, 4x cm, 5x cm.
The diagonal of new cube is
We need to find the edges of three cubes
Here, volume of the resulting cube,
Let,
Edge of the resulting cube
So, diagonal of the cube , so
Hence,
Now;
The edges of the three cubes are,
The edges of the three cubes are .
Q u e s t i o n : 5 0
If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the
base of a cube are called its lateral faces.
S o l u t i o n :
Let,
Side of the cube
Perimeter of each face is 32 cm.
Lateral surface area,
So the lateral surface area of the cube is .
Q u e s t i o n : 5 1
Find the edge of a cube whose surface area is 432 m
2
.
S o l u t i o n :
Let,
Edge of the cube
Surface area of the cube = 6a
2
So,
Side of the cube is .
Q u e s t i o n : 5 2
A cuboid has total surface area of 372 cm
2
and its lateral surface area is 180 cm
2
, find the area of its base.
S o l u t i o n :
We have,
Total surface area of the cuboid
Page 4
Q u e s t i o n : 4 8
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
S o l u t i o n :
We have,
Side of each cube (a) = 6 cm
We need to find the volume of resulting cuboid
Hence, dimensions of the resulting cuboid are,
Length (l) = 2a
Breadth (b) = a
= 6 cm
Height (h) = a
= 6 cm
Hence, volume of the resulting cuboid,
Hence, volume of the resulting cuboid is .
Q u e s t i o n : 4 9
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is
12
v
3
cm. Find the edges of three cubes.
S o l u t i o n :
The edges of the three cubes are in the ratio 3 : 4 : 5.
So, let the edges be 3x cm, 4x cm, 5x cm.
The diagonal of new cube is
We need to find the edges of three cubes
Here, volume of the resulting cube,
Let,
Edge of the resulting cube
So, diagonal of the cube , so
Hence,
Now;
The edges of the three cubes are,
The edges of the three cubes are .
Q u e s t i o n : 5 0
If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the
base of a cube are called its lateral faces.
S o l u t i o n :
Let,
Side of the cube
Perimeter of each face is 32 cm.
Lateral surface area,
So the lateral surface area of the cube is .
Q u e s t i o n : 5 1
Find the edge of a cube whose surface area is 432 m
2
.
S o l u t i o n :
Let,
Edge of the cube
Surface area of the cube = 6a
2
So,
Side of the cube is .
Q u e s t i o n : 5 2
A cuboid has total surface area of 372 cm
2
and its lateral surface area is 180 cm
2
, find the area of its base.
S o l u t i o n :
We have,
Total surface area of the cuboid
Lateral surface area of the cuboid
Let,
Area of the base
We know that,
Area of the base is .
Q u e s t i o n : 5 3
Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
S o l u t i o n :
Side of each cube (a) = 4 cm
We need to find the surface area of the resulting cuboid
Dimensions of the resulting cuboid,
Length (l) = 3a
Breadth (b) = a
Height (h) = a
Surface area of the cuboid,
Surface area of the cuboid is .
Q u e s t i o n : 5 4
The surface area of a cuboid is 1300 cm
2
. If its breadth is 10 cm and height is 20 cm
2
, find its length.
S o l u t i o n :
Let, l ? Length of the cuboid
Breadth of the cuboid (b) = 10 cm
Height of the cuboid (h) = 20 cm
Surface area of the cuboid (A) = 1300 cm
2
Page 5
Q u e s t i o n : 4 8
If two cubes each of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
S o l u t i o n :
We have,
Side of each cube (a) = 6 cm
We need to find the volume of resulting cuboid
Hence, dimensions of the resulting cuboid are,
Length (l) = 2a
Breadth (b) = a
= 6 cm
Height (h) = a
= 6 cm
Hence, volume of the resulting cuboid,
Hence, volume of the resulting cuboid is .
Q u e s t i o n : 4 9
Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down in to a single cube whose diagonal is
12
v
3
cm. Find the edges of three cubes.
S o l u t i o n :
The edges of the three cubes are in the ratio 3 : 4 : 5.
So, let the edges be 3x cm, 4x cm, 5x cm.
The diagonal of new cube is
We need to find the edges of three cubes
Here, volume of the resulting cube,
Let,
Edge of the resulting cube
So, diagonal of the cube , so
Hence,
Now;
The edges of the three cubes are,
The edges of the three cubes are .
Q u e s t i o n : 5 0
If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the
base of a cube are called its lateral faces.
S o l u t i o n :
Let,
Side of the cube
Perimeter of each face is 32 cm.
Lateral surface area,
So the lateral surface area of the cube is .
Q u e s t i o n : 5 1
Find the edge of a cube whose surface area is 432 m
2
.
S o l u t i o n :
Let,
Edge of the cube
Surface area of the cube = 6a
2
So,
Side of the cube is .
Q u e s t i o n : 5 2
A cuboid has total surface area of 372 cm
2
and its lateral surface area is 180 cm
2
, find the area of its base.
S o l u t i o n :
We have,
Total surface area of the cuboid
Lateral surface area of the cuboid
Let,
Area of the base
We know that,
Area of the base is .
Q u e s t i o n : 5 3
Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
S o l u t i o n :
Side of each cube (a) = 4 cm
We need to find the surface area of the resulting cuboid
Dimensions of the resulting cuboid,
Length (l) = 3a
Breadth (b) = a
Height (h) = a
Surface area of the cuboid,
Surface area of the cuboid is .
Q u e s t i o n : 5 4
The surface area of a cuboid is 1300 cm
2
. If its breadth is 10 cm and height is 20 cm
2
, find its length.
S o l u t i o n :
Let, l ? Length of the cuboid
Breadth of the cuboid (b) = 10 cm
Height of the cuboid (h) = 20 cm
Surface area of the cuboid (A) = 1300 cm
2
We have to find the length of the cuboid
We know that,
Length of the cuboid is .
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FAQs on Class 9 Maths Question Answers - Surface Area and Volume of a Cuboid and Cube
| 1. What is the formula to calculate the surface area of a cuboid? |  |
Ans. The formula to calculate the surface area of a cuboid is 2(lw + lh + wh), where l, w, and h are the length, width, and height of the cuboid, respectively.
| 2. How do you find the volume of a cube? | |
Ans. The volume of a cube can be found by raising the length of one side to the power of 3. So, the formula for the volume of a cube is V = s^3, where s represents the length of a side.
| 3. Can the surface area of a cuboid be greater than its volume? | |
Ans. No, it is not possible for the surface area of a cuboid to be greater than its volume. The surface area represents the total area of the six faces of the cuboid, whereas the volume represents the space enclosed by the cuboid. Since surface area is measured in square units and volume is measured in cubic units, the volume will always be greater than or equal to the surface area.
| 4. How can we calculate the length of a side of a cube if we know its volume? | |
Ans. To calculate the length of a side of a cube if we know its volume, we can take the cube root of the volume. So, if V is the volume of the cube, then the length of a side can be found using the formula s = ∛V.
| 5. Can a cuboid and a cube have the same volume but different surface areas? | |
Ans. Yes, it is possible for a cuboid and a cube to have the same volume but different surface areas. Since the volume only depends on the length of the sides, different combinations of length, width, and height can result in the same volume. However, the surface area also takes into account the shape and arrangement of the sides, so different dimensions can lead to different surface areas.
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Nov 22, 2024 Last updated |
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