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All questions of Surface Area, Volume and Capacity (Cuboid, Cube and Cylinder) for Class 8 Exam
What is the curved surface area of a cylinder with a height of 12 cm and a radius of 3 cm?- a)113.04 cm²
- b)226.08 cm²
- c)150.72 cm²
- d)75.36 cm²
Correct answer is option 'B'. Can you explain this answer?
What is the curved surface area of a cylinder with a height of 12 cm and a radius of 3 cm?
a)
113.04 cm²
b)
226.08 cm²
c)
150.72 cm²
d)
75.36 cm²
 | Get Idea answered |
The curved surface area is calculated using the formula 2πrh. Substituting the values, Curved Surface Area = 2 × π × 3 cm × 12 cm = 226.08 cm².
A room has dimensions of 5 m × 4 m × 3 m. What is the total surface area of the room (excluding the floor)?- a)60 m²
- b)66 m²
- c)54 m²
- d)78 m²
Correct answer is option 'C'. Can you explain this answer?
A room has dimensions of 5 m × 4 m × 3 m. What is the total surface area of the room (excluding the floor)?
a)
60 m²
b)
66 m²
c)
54 m²
d)
78 m²
 | Yashvi Iyer answered |
Understanding Room Dimensions
The room has dimensions of 5 m (length) × 4 m (width) × 3 m (height). To find the total surface area while excluding the floor, we will calculate the areas of the four walls and the ceiling.
Calculating the Areas of Walls
1. Area of Two Longer Walls (Length × Height):
- Each wall's area = Length × Height = 5 m × 3 m = 15 m²
- Total for two walls = 2 × 15 m² = 30 m²
2. Area of Two Shorter Walls (Width × Height):
- Each wall's area = Width × Height = 4 m × 3 m = 12 m²
- Total for two walls = 2 × 12 m² = 24 m²
Calculating the Area of the Ceiling
3. Area of the Ceiling (Length × Width):
- Ceiling area = Length × Width = 5 m × 4 m = 20 m²
Summing Up the Areas
4. Total Surface Area Calculation:
- Total wall area = Area of longer walls + Area of shorter walls = 30 m² + 24 m² = 54 m²
- Adding the ceiling area = Total wall area + Ceiling area = 54 m² + 20 m² = 74 m²
However, since we need to exclude the floor, we only consider the walls and the ceiling:
Final Calculation
- Total area excluding the floor = 54 m² (walls) + 20 m² (ceiling) = 74 m²
Conclusion
The total surface area of the room, excluding the floor, is 54 m². Therefore, the correct answer is option 'C'.
The room has dimensions of 5 m (length) × 4 m (width) × 3 m (height). To find the total surface area while excluding the floor, we will calculate the areas of the four walls and the ceiling.
Calculating the Areas of Walls
1. Area of Two Longer Walls (Length × Height):
- Each wall's area = Length × Height = 5 m × 3 m = 15 m²
- Total for two walls = 2 × 15 m² = 30 m²
2. Area of Two Shorter Walls (Width × Height):
- Each wall's area = Width × Height = 4 m × 3 m = 12 m²
- Total for two walls = 2 × 12 m² = 24 m²
Calculating the Area of the Ceiling
3. Area of the Ceiling (Length × Width):
- Ceiling area = Length × Width = 5 m × 4 m = 20 m²
Summing Up the Areas
4. Total Surface Area Calculation:
- Total wall area = Area of longer walls + Area of shorter walls = 30 m² + 24 m² = 54 m²
- Adding the ceiling area = Total wall area + Ceiling area = 54 m² + 20 m² = 74 m²
However, since we need to exclude the floor, we only consider the walls and the ceiling:
Final Calculation
- Total area excluding the floor = 54 m² (walls) + 20 m² (ceiling) = 74 m²
Conclusion
The total surface area of the room, excluding the floor, is 54 m². Therefore, the correct answer is option 'C'.
A room's walls need to be painted. If the room is 3 m high with dimensions of 4 m by 5 m, what is the area of the walls to be painted?- a)50 m²
- b)45 m²
- c)30 m²
- d)40 m²
Correct answer is option 'A'. Can you explain this answer?
A room's walls need to be painted. If the room is 3 m high with dimensions of 4 m by 5 m, what is the area of the walls to be painted?
a)
50 m²
b)
45 m²
c)
30 m²
d)
40 m²
| | Get Idea answered |
The area of the walls is calculated as 2 × (Length + Width) × Height = 2 × (4 + 5) × 3 = 54 m².
What is the relationship between capacity and volume for a container?- a)Volume is the total space a container occupies, while capacity is the internal volume.
- b)Capacity is a measure of the weight of a container.
- c)Capacity is always greater than volume.
- d)Capacity and volume are the same.
Correct answer is option 'A'. Can you explain this answer?
What is the relationship between capacity and volume for a container?
a)
Volume is the total space a container occupies, while capacity is the internal volume.
b)
Capacity is a measure of the weight of a container.
c)
Capacity is always greater than volume.
d)
Capacity and volume are the same.
| | Get Idea answered |
Volume refers to the total space occupied by the solid material of the container, while capacity refers specifically to the internal volume available for holding liquids or gases.
What is the formula used to calculate the volume of a cuboid?- a)Length × Width × Height
- b)Length + Width + Height
- c)2(Length + Width + Height)
- d)Length × Width
Correct answer is option 'A'. Can you explain this answer?
What is the formula used to calculate the volume of a cuboid?
a)
Length × Width × Height
b)
Length + Width + Height
c)
2(Length + Width + Height)
d)
Length × Width
| | Get Idea answered |
The volume of a cuboid is calculated using the formula Volume = Length × Width × Height. This formula reflects the three dimensions of the cuboid, allowing us to determine the total space it occupies.
What is the total surface area of a cuboid with dimensions 2 m, 3 m, and 4 m?- a)24 m²
- b)28 m²
- c)32 m²
- d)20 m²
Correct answer is option 'C'. Can you explain this answer?
What is the total surface area of a cuboid with dimensions 2 m, 3 m, and 4 m?
a)
24 m²
b)
28 m²
c)
32 m²
d)
20 m²
| | Get Idea answered |
The total surface area is calculated by the formula 2(lb + bh + hl). Substituting gives 2(2 × 3 + 3 × 4 + 4 × 2) = 2(6 + 12 + 8) = 2(26) = 52 m².
A cylinder has a height of 15 cm and a volume of 1,050 cm³. What is the radius of its base?- a)8 cm
- b)7 cm
- c)5 cm
- d)10 cm
Correct answer is option 'B'. Can you explain this answer?
A cylinder has a height of 15 cm and a volume of 1,050 cm³. What is the radius of its base?
a)
8 cm
b)
7 cm
c)
5 cm
d)
10 cm
| | Get Idea answered |
The formula for volume is V = πr²h. Rearranging gives r = √(V/(πh)). Substituting the values, r = √(1050/(π × 15)) ≈ 7 cm.
How many liters are in 1 cubic meter?- a)1,000 liters
- b)200 liters
- c)2,000 liters
- d)500 liters
Correct answer is option 'A'. Can you explain this answer?
How many liters are in 1 cubic meter?
a)
1,000 liters
b)
200 liters
c)
2,000 liters
d)
500 liters
| | Get Idea answered |
1 cubic meter is equivalent to 1,000 liters. This equivalence is important in conversions for various applications, particularly in water storage and utility measurements.
What is the formula for the total surface area of a cylinder?- a)2πrh + 2πr²
- b)πr²h
- c)2πr(h + r)
- d)πd²/4
Correct answer is option 'A'. Can you explain this answer?
What is the formula for the total surface area of a cylinder?
a)
2πrh + 2πr²
b)
πr²h
c)
2πr(h + r)
d)
πd²/4
| | Get Idea answered |
The total surface area of a cylinder is given by the formula Total Surface Area = 2πrh + 2πr², which includes both the curved surface area and the areas of the two circular bases.
What is the internal volume of a closed box with external dimensions of 30 cm × 20 cm × 15 cm and a wall thickness of 1 cm?- a)5,000 cm³
- b)6,000 cm³
- c)3,000 cm³
- d)4,000 cm³
Correct answer is option 'B'. Can you explain this answer?
What is the internal volume of a closed box with external dimensions of 30 cm × 20 cm × 15 cm and a wall thickness of 1 cm?
a)
5,000 cm³
b)
6,000 cm³
c)
3,000 cm³
d)
4,000 cm³
| | Get Idea answered |
To find the internal volume, first calculate the internal dimensions: Length = 30 - 2(1) = 28 cm, Breadth = 20 - 2(1) = 18 cm, Height = 15 - 2(1) = 13 cm. Therefore, the internal volume = 28 × 18 × 13 = 6,072 cm³.
What are the internal dimensions of a box with external dimensions of 50 cm × 40 cm × 30 cm and wall thickness of 3 cm?- a)45 cm × 35 cm × 25 cm
- b)47 cm × 37 cm × 27 cm
- c)48 cm × 38 cm × 28 cm
- d)44 cm × 34 cm × 24 cm
Correct answer is option 'D'. Can you explain this answer?
What are the internal dimensions of a box with external dimensions of 50 cm × 40 cm × 30 cm and wall thickness of 3 cm?
a)
45 cm × 35 cm × 25 cm
b)
47 cm × 37 cm × 27 cm
c)
48 cm × 38 cm × 28 cm
d)
44 cm × 34 cm × 24 cm
| | Get Idea answered |
To find the internal dimensions, subtract twice the thickness from each external dimension: Length = 50 - 2(3) = 44 cm, Breadth = 40 - 2(3) = 34 cm, Height = 30 - 2(3) = 24 cm.
If a cylinder has a radius of 7 cm and a height of 10 cm, what is its volume?- a)770 cm³
- b)490 cm³
- c)2200 cm³
- d)1540 cm³
Correct answer is option 'D'. Can you explain this answer?
If a cylinder has a radius of 7 cm and a height of 10 cm, what is its volume?
a)
770 cm³
b)
490 cm³
c)
2200 cm³
d)
1540 cm³
| | Get Idea answered |
The volume of a cylinder is given by V = πr²h. Using π ≈ 3.14, V = 3.14 × (7 cm)² × 10 cm = 3.14 × 49 × 10 ≈ 1539.4 cm³, which rounds to approximately 1540 cm³.
What is the total surface area of a cube with an edge length of 4 cm?- a)24 cm²
- b)36 cm²
- c)96 cm²
- d)48 cm²
Correct answer is option 'C'. Can you explain this answer?
What is the total surface area of a cube with an edge length of 4 cm?
a)
24 cm²
b)
36 cm²
c)
96 cm²
d)
48 cm²
| | Get Idea answered |
The total surface area of a cube is calculated using the formula Total Surface Area = 6 × (Edge Length)². For a cube with an edge of 4 cm, the total surface area is 6 × (4 cm)² = 6 × 16 cm² = 96 cm².
Which unit is typically used to express the volume of a solid object?- a)Square meters (m²)
- b)Cubic centimeters (cm³)
- c)Inches (in)
- d)Liters (L)
Correct answer is option 'B'. Can you explain this answer?
Which unit is typically used to express the volume of a solid object?
a)
Square meters (m²)
b)
Cubic centimeters (cm³)
c)
Inches (in)
d)
Liters (L)
| | Get Idea answered |
Volume is generally expressed in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). This measurement accounts for the three-dimensional space an object occupies.
If the surface area of a cube is 216 cm², what is the length of one edge?- a)8 cm
- b)9 cm
- c)12 cm
- d)6 cm
Correct answer is option 'D'. Can you explain this answer?
If the surface area of a cube is 216 cm², what is the length of one edge?
a)
8 cm
b)
9 cm
c)
12 cm
d)
6 cm
| | Get Idea answered |
The total surface area of a cube is given by 6a². Setting 6a² = 216 gives a² = 36, so a = 6 cm. Each edge of the cube is 6 cm long.
What is the formula for the volume of a cube whose edge length is 'a'?- a)6a
- b)a³
- c)2a
- d)a²
Correct answer is option 'B'. Can you explain this answer?
What is the formula for the volume of a cube whose edge length is 'a'?
a)
6a
b)
a³
c)
2a
d)
a²
| | Get Idea answered |
The volume of a cube is calculated using the formula Volume = a³, where 'a' is the length of one edge. This formula highlights the property of cubes where all sides are equal.
A box's external dimensions are 12 cm, 10 cm, and 8 cm, with a wall thickness of 1 cm. What is the volume of the material used for the box?- a)120 cm³
- b)80 cm³
- c)160 cm³
- d)100 cm³
Correct answer is option 'C'. Can you explain this answer?
A box's external dimensions are 12 cm, 10 cm, and 8 cm, with a wall thickness of 1 cm. What is the volume of the material used for the box?
a)
120 cm³
b)
80 cm³
c)
160 cm³
d)
100 cm³
| | Get Idea answered |
First, calculate the external volume: 12 × 10 × 8 = 960 cm³. Then, calculate the internal dimensions: 10 × 8 × 6 = 480 cm³. The volume of the material is 960 - 480 = 480 cm³.
If the capacity of a container is 2 liters, what is this value in cubic centimeters?- a)200 cm³
- b)20,000 cm³
- c)1,000 cm³
- d)2,000 cm³
Correct answer is option 'D'. Can you explain this answer?
If the capacity of a container is 2 liters, what is this value in cubic centimeters?
a)
200 cm³
b)
20,000 cm³
c)
1,000 cm³
d)
2,000 cm³
| | Get Idea answered |
Since 1 liter is equivalent to 1,000 cm³, a capacity of 2 liters equals 2 × 1,000 cm³ = 2,000 cm³. This conversion is crucial in various applications, including cooking and laboratory settings.
The dimensions of a cuboid are in the ratio 2:3:4. If the volume is 120 cm³, what is the length of the longest side?- a)14 cm
- b)12 cm
- c)8 cm
- d)10 cm
Correct answer is option 'C'. Can you explain this answer?
The dimensions of a cuboid are in the ratio 2:3:4. If the volume is 120 cm³, what is the length of the longest side?
a)
14 cm
b)
12 cm
c)
8 cm
d)
10 cm
| | Get Idea answered |
Let the dimensions be 2x, 3x, and 4x. The volume V = 2x × 3x × 4x = 24x³. Setting 24x³ = 120 gives x³ = 5, thus x = 1.71. The longest side = 4x = 6.86 cm, rounding gives approximately 8 cm.
If a block of wood has a length of 10 cm, width of 5 cm, and height of 2 cm, what is its volume?- a)200 cm³
- b)50 cm³
- c)150 cm³
- d)100 cm³
Correct answer is option 'D'. Can you explain this answer?
If a block of wood has a length of 10 cm, width of 5 cm, and height of 2 cm, what is its volume?
a)
200 cm³
b)
50 cm³
c)
150 cm³
d)
100 cm³
| | Get Idea answered |
The volume of the block is calculated as Volume = Length × Width × Height = 10 cm × 5 cm × 2 cm = 100 cm³.
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