Volume Of Cube Cuboid And Cylinder

To determine which statements are incorrect regarding the volume formulas, let's evaluate each one based on standard mathematical knowledge.

(A) Volume of a cone =

(B) Volume of a cone =

(C) Volume of a hemisphere =

(D) Volume of a hemisphere =

(E) Volume of a cylinder =

Let's analyze each statement:

Conclusion: From the given options, the only statement identified as correct is statement (A), as options (B), (C), and (E) are incorrect. Therefore, the correct answer is Only argument (A) is strong.

The problem requires us to determine the volume of a cube given that the perimeter of one face is 24 cm. A cube has six faces, each a square, and the perimeter of a square is four times the side length. Therefore, if the perimeter of one face is 24 cm, we use the formula:

P = 4s

where P is the perimeter, and s is the side length. Substituting the given perimeter:

24 = 4s

Solving for s:

s = 24/4 = 6 cm

Next, the volume V of a cube is calculated as:

V = s³

Substituting the side length:

V = 6³ = 6 × 6 × 6 = 216 cm³

The volume of the cube is therefore 216 cm³, which matches the given correct answer option.

To determine the number of bricks required to build a wall, we start by calculating the volume of the wall and the volume of a single brick. The number of bricks can then be found by dividing the wall's volume by the brick's volume.

Dimensions of the wall: length = 10 m, height = 4 m, thickness = 24 cm

Convert the wall's dimensions to the same unit (cm) for consistency:

Length = 10 m = 1000 cm

Height = 4 m = 400 cm

Thickness = 24 cm

Volume of the wall = length × height × thickness = 1000 cm × 400 cm × 24 cm = 9600000 cm³

Dimensions of a brick: 25 cm × 12 cm × 8 cm

Volume of a brick = 25 cm × 12 cm × 8 cm = 2400 cm³

Number of bricks = Volume of the wall / Volume of a brick = 9600000 cm³ / 2400 cm³

Number of bricks = 4000

Thus, the number of bricks required is 4000.

To determine which statements are incorrect, we need to know the correct formulas for the volumes of different geometric shapes:

• The volume of a cone is given by: .
• The volume of a hemisphere is given by: .
• The volume of a cylinder is given by: .

Now, let's evaluate the provided statements:

1. (A) Volume of a cone = :
   The correct formula is , so this statement is incorrect.
2. (B) Volume of a cone = :
   This matches the correct formula, so this statement is correct.
3. (C) Volume of a hemisphere = :
   The correct formula is , so this statement is incorrect.
4. (D) Volume of a hemisphere = :
   This matches the correct formula, so this statement is correct.
5. (E) Volume of a cylinder = :
   The correct formula is , so this statement is incorrect.

Based on above evaluation, the incorrect statements are (A), (C), and (E). Therefore, the correct option is:

To determine the maximum volume of an open box with a square base made from a cardboard of area , let's follow these steps:

1. Define the variables: Let the side of the square base be and the height of the box be . The area of the cardboard forms the base and four sides, so:

2. Solve for :

3. The volume of the box is given by:

4. Differentiating with respect to and setting the derivative equal to zero to find the critical points:

Setting :

5. Substitute back into the equation for :

6. Now substitute and back into the volume equation:

Thus, the maximum volume of the box is .