Cube Surface Area Calculation from Volume
This problem requires us to find the total surface area of a cube when we know its volume. We need to use the relationship between a cube's volume, its side length, and its total surface area.
Understanding Cube Properties
A cube is a three-dimensional shape with six equal square faces. All its edges (sides) have the same length.
- Let the length of one side of the cube be denoted by '$s$'.
- The volume ($V$) of a cube is calculated by cubing the side length: $V = s^3$.
- The total surface area (TSA) of a cube is the sum of the areas of its six faces. Since each face is a square with area $s^2$, the total surface area is: $TSA = 6 \times s^2$.
Step 1: Find the Side Length from the Volume
We are given that the volume of the cube is 64 cm³. We can use the volume formula to find the side length '$s$'.
Given:
$V = 64 \text{ cm}^3$Using the formula $V = s^3$:
$s^3 = 64 \text{ cm}^3$To find '$s$', we need to take the cube root of 64:
$s = \sqrt[3]{64 \text{ cm}^3}$ $s = 4 \text{ cm}$So, the length of each side of the cube is 4 cm.
Step 2: Calculate the Total Surface Area
Now that we know the side length ('$s = 4$ cm'), we can calculate the total surface area using the formula $TSA = 6s^2$.
Calculation:
$TSA = 6 \times (4 \text{ cm})^2$ $TSA = 6 \times (16 \text{ cm}^2)$ $TSA = 96 \text{ cm}^2$Conclusion
The total surface area of the cube is 96 cm².
Similar Questions
- Find the surface area of a ball of radius 21 mm. (Use $\pi = \frac{22}{7}$)
- The dimensions of a pond are 20 m, 14 m and 6 m. Find the capacity of the pond.
Important Questions from Mensuration
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
