All questions of Mensuration for Class 8 Exam

Sol. perimeter of square=4* sides
=4*4 (sides is 4)
=16.

Finding Volume of a Cuboid

Given: length = 8 cm, width = 3 cm, height = 5 cm

To find: Volume of the cuboid

Formula: Volume of a cuboid = length x width x height

Substituting the given values in the formula, we get:

Volume = 8 cm x 3 cm x 5 cm

Volume = 120 cm3

Therefore, the correct answer is option C, 120 cm3.

Given,
Length (l) = 8 cm
Breadth (b) = 6 cm
Height (h) = 3.5 cm

We know that the volume of a cuboid is given by the formula:
Volume = length × breadth × height

Substituting the given values, we get:
Volume = 8 cm × 6 cm × 3.5 cm
Volume = 168 cm³

Therefore, the volume of the given cuboid is 168 cm³.

Hence, the correct option is (d) 168 cm³.

Explanation:

A cuboid is a 3-dimensional figure that has six rectangular faces. The lateral surface area of a cuboid is the area of the four vertical rectangular faces, excluding the top and bottom faces.

Let's consider a cuboid with length (l), breadth (b) and height (h).

Formula for Lateral Surface Area of Cuboid:
The formula for the lateral surface area of a cuboid is:

Lateral Surface Area of Cuboid = 2h(l+b)

Proof:
To find the lateral surface area of a cuboid, we need to add the areas of all the four vertical rectangular faces.

- The area of the first vertical face = l x h
- The area of the second vertical face = b x h
- The area of the third vertical face = l x h
- The area of the fourth vertical face = b x h

Adding all these areas, we get:

Lateral Surface Area of Cuboid = lh + bh + lh + bh
= 2lh + 2bh
= 2h(l+b)

Therefore, the formula for the lateral surface area of a cuboid is 2h(l+b).

Finding the Height of a Cuboid

Given information: Volume = 200 cm³, Base Area = 20 cm²

To find: Height of the cuboid

Formula to find the volume of a cuboid: V = l × b × h, where l is the length, b is the breadth, and h is the height of the cuboid.

Formula to find the base area of a cuboid: A = l × b

We are given that the volume of the cuboid is 200 cm³. Therefore, we can write:

l × b × h = 200

We are also given that the base area of the cuboid is 20 cm². Therefore, we can write:

l × b = 20

Solving the above two equations, we get:

h = 200 / (l × b)

l × b = 20

h = 200 / 20

h = 10 cm

Therefore, the height of the cuboid is 10 cm.

Answer: Option (c) 10 cm.

Total Surface Area of a Cylinder
To find the total surface area of a right circular cylinder, we use the formula:
Total Surface Area (TSA) = 2πr(h + r)
Where:
- r = radius of the base
- h = height of the cylinder
Given Values
- Radius (r) = 5 cm
- Height (h) = 10 cm
Calculating the Total Surface Area
1. Substituting the values:
- TSA = 2π(5 cm)(10 cm + 5 cm)
2. Calculating the height plus radius:
- h + r = 10 cm + 5 cm = 15 cm
3. Continuing with the formula:
- TSA = 2π(5 cm)(15 cm)
4. Perform the multiplication:
- TSA = 2π(75 cm²)
- TSA = 150π cm²
Conclusion
Thus, the total surface area of the cylinder is 150π cm².
The correct answer is option 'A' (150π cm²).
This formula effectively combines the lateral surface area and the area of the two circular bases, giving a complete picture of the cylinder's surface.

Explanation:

When we double the edge of a cube, we are essentially multiplying the length of each edge by 2. Let the original edge length be l. After doubling the edge, new edge length will be 2l.

Calculating the surface area of the original cube:

The surface area of a cube is given by the formula 6l^2, where l is the length of an edge. Here, l is the original edge length. So, the surface area of the original cube is 6l^2.

Calculating the surface area of the doubled cube:

The surface area of the doubled cube is given by the formula 6(2l)^2, since each edge length is now 2l. Simplifying this expression, we get:

6(2l)^2 = 6(4l^2) = 24l^2

So, the surface area of the doubled cube is 24l^2.

Calculating the ratio of the surface areas:

To find the ratio of the surface areas, we need to divide the surface area of the doubled cube by the surface area of the original cube:

(24l^2) / (6l^2) = 4

So, the surface area of the doubled cube is 4 times the surface area of the original cube.

Conclusion:

Therefore, the correct option is C, that is, the surface area of the cube will increase four times if each edge of a cube is doubled.

Explanation:
To find the total surface area of a cube, we need to find the area of all its six faces and add them up. Since all the faces of a cube are identical squares, we can find the area of one face and multiply it by 6 to get the total surface area.

Given, the edge of the cube is 1 cm. Therefore, the area of one face of the cube is:

Area of square = side × side
Area of square = 1 cm × 1 cm
Area of square = 1 cm²

To find the total surface area of the cube, we need to multiply the area of one face by 6:

Total surface area of cube = 6 × area of one face
Total surface area of cube = 6 × 1 cm²
Total surface area of cube = 6 cm²

Therefore, the total surface area of the cube is 6 cm², which is option C.

Understanding the Problem
To find the height of a cuboid given its volume and base area, we can use the formula for the volume of a cuboid:
- Volume = Base Area × Height
In this case, we know the following:
- Volume = 275 cm³
- Base Area = 25 cm²
Finding the Height
We can rearrange the formula to solve for height:
- Height = Volume / Base Area
Now, substituting the known values:
- Height = 275 cm³ / 25 cm²
Performing the Calculation
Now we perform the division:
- Height = 275 / 25
- Height = 11 cm
Conclusion
Thus, the height of the cuboid is:
- 11 cm
The correct answer is option 'B'.

Understanding the Problem
We have a square park and a circular park with the same area. The side of the square park is given as 14 meters. We need to find the radius of the circular park.
Calculating the Area of the Square Park
- The area of a square is calculated using the formula:
Area = side × side
- Given that the side is 14 meters:
Area of square = 14 m × 14 m = 196 m²
Setting the Area of the Circular Park
- Since the areas are equal, the area of the circular park is also 196 m².
- The formula for the area of a circle is:
Area = π × r², where r is the radius of the circle.
Finding the Radius of the Circular Park
- We set the area of the circle equal to 196 m²:
π × r² = 196
- Rearranging gives us:
r² = 196 / π
Calculating the Approximate Radius
- Using π ≈ 3.14:
r² ≈ 196 / 3.14 ≈ 62.43
- To find r, take the square root:
r ≈ √62.43 ≈ 7.9 m
Conclusion
- The radius of the circular park is approximately 8 meters.
- Therefore, the correct answer is option 'B'.
This calculation shows how to equate areas and solve for the radius of the circular park based on the given dimensions of the square park.