The difference between the total surface area and lateral surface area of a cube, if side of the cube is 11 cm (in square cm), is ___________.
Cube Difference Calculation
This problem requires finding the difference between the total surface area and the lateral surface area of a cube with a given side length of 11 cm.
Understanding the terms:
- A cube is a 3D shape with six identical square faces.
- Total Surface Area (TSA) refers to the sum of the areas of all six faces.
- Lateral Surface Area (LSA) refers to the sum of the areas of the four vertical faces, excluding the top and bottom faces.
Cube Surface Area Formulas
Let '$a$' represent the length of one side of the cube. The formulas for the surface areas are:
- Total Surface Area (TSA): $TSA = 6a^2$
- Lateral Surface Area (LSA): $LSA = 4a^2$
Deriving the Difference Formula
The question asks for the difference between TSA and LSA.
Difference = TSA - LSA
Substituting the formulas into the equation:
Difference = $6a^2 - 4a^2$
By simplifying the expression, we get:
Difference = $2a^2$
This result indicates that the difference in surface area is equivalent to the area of two faces of the cube.
Applying Side Length 11 cm
We are given that the side length of the cube is $a = 11$ cm.
Using the simplified formula for the difference, $2a^2$, we can calculate the value:
Difference = $2 \times (11 \text{ cm})^2$
First, calculate the square of the side length:
$(11 \text{ cm})^2 = 11 \times 11 \text{ cm}^2 = 121 \text{ cm}^2$
Next, multiply this result by 2:
Difference = $2 \times 121 \text{ cm}^2 = 242 \text{ cm}^2$
Calculation Steps & Verification
To confirm the result, we can calculate the TSA and LSA separately using the given side length ($a = 11$ cm).
1. Calculate Total Surface Area (TSA):
$TSA = 6a^2 = 6 \times (11 \text{ cm})^2 = 6 \times 121 \text{ cm}^2 = 726 \text{ cm}^2$
2. Calculate Lateral Surface Area (LSA):
$LSA = 4a^2 = 4 \times (11 \text{ cm})^2 = 4 \times 121 \text{ cm}^2 = 484 \text{ cm}^2$
3. Compute the Difference:
Difference = $TSA - LSA = 726 \text{ cm}^2 - 484 \text{ cm}^2 = 242 \text{ cm}^2$
Both calculation methods confirm that the difference is 242 square centimeters.
Similar Questions
- The area of the rhombus (in $cm^2$) having each side equal to 13 cm and one of its diagonals equal to 24 cm is:
- If the length of each of the two equal sides of an isosceles triangle is 15 cm and the adjacent angle is 30°, then the area of the triangle is:
- Find the surface area of a ball of radius 21 mm. (Use $\pi = \frac{22}{7}$)
A hemispherical bowl has a 21 cm radius. It is to be painted inside as well as outside. The cost of painting it at the rate of ₹0.05 per $cm^2$ and assuming that the thickness of the bowl is negligible, is: (Use $\pi = \frac{22}{7}$)
- The volume of a right circular cylinder of base radius r is obtained by multiplying its curved surface area by:
- The radius of a cylinder is 7 feet. Find the total surface area of the cylinder if the height of the cylinder is 14 feet. (Use $\pi = \frac{22}{7}$)
- If the volume of spheres are 27: 8, then their ratio of surface areas is:
- A hemisphere has 14 cm diameter. Find its volume.
- The perimeter of the rectangle is 280 m and the difference between its two sides is 40 m. Find the side of a square whose area is equal to the area of this rectangle.
- A cone with radius 7 m is 6 m high. Find the volume (in $m^3$) of the cone.
(Take $\pi = \frac{22}{7}$)
Important Questions from Mensuration
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?
A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden
A village having a population of 4000 requires 150 liters of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for
The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is
