Cube Volume Calculation from Painting Cost
The problem asks for the volume of a cube, given the total cost of painting all its external surfaces and the painting rate.
Step 1: Calculate the Total Surface Area (TSA)
First, find the total surface area that was painted. This is done by dividing the total cost by the rate per square centimeter.
- Total Cost = ₹588
- Rate = ₹2/cm$^2$
-
Total Surface Area (TSA) = $\frac{\text{Total Cost}}{\text{Rate}}$
TSA = $\frac{₹588}{₹2/\text{cm}^2}$ = 294 cm$^2$
Step 2: Determine the Side Length of the Cube
The formula for the total surface area of a cube with side length '$a$' is $6a^2$. We use the TSA calculated in Step 1 to find '$a$'.
- TSA = $6a^2$
- $294 \text{ cm}^2 = 6a^2$
- $a^2 = \frac{294 \text{ cm}^2}{6}$
- $a^2 = 49 \text{ cm}^2$
- $a = \sqrt{49 \text{ cm}^2}$
- $a = 7 \text{ cm}$
Step 3: Calculate the Volume of the Cube
Finally, calculate the volume of the cube using the side length '$a$' found in Step 2. The formula for the volume (V) of a cube is $a^3$.
- Volume (V) = $a^3$
- V = $(7 \text{ cm})^3$
- V = $7 \times 7 \times 7$ cm$^3$
- V = 343 cm$^3$
The volume of the cube is 343 cm$^3$. This matches option B.
Similar Questions
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Important Questions from 3-D Mensuration
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
The length and breadth of a cuboid are 50 cm and 75 cm, respectively. If the length of the diagonal is $17\sqrt{29}$ cm, then what is the volume (in $cm^{3}$) of the cuboid?
