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
- The radius of a sphere is 16 cm. Find its surface area.
- The total surface area of a cube having side 40 cm is:
- The length, breadth and height of a cuboid are in the ratio of 5 : 4 : 3. If the sum of the length, breadth and height is 120 cm, then what will be its volume?
- A cuboid has length 10 cm, breadth 5 cm and height 2 cm. What is its surface area?
- The curve surface area of a cylindrical pillar is $264\text{ m}^2$ and its volume is $924\text{ m}^3$. Find the ratio of its height to its diameter.
- Find the total surface area of a cone, if its radius and slant height are $2r$ and $\frac{1}{2}$ respectively.
- If the surface area of a cube is $1014\text{ m}^{2}$, then its volume is:
- Five solid cubes, each of volume $39304 \text{ cm}^3$, are joined end to end to form a cuboid. What is the lateral surface area (in $\text{cm}^2$) of the cuboid?
- Find the surface area of a sphere whose diameter is equal to 54 cm.
- What is the surface area of a sphere of radius 8 cm? (use $\pi = 3.14$)
Important Questions from 3-D Mensuration
- Find the surface area of a sphere whose diameter is equal to 98 cm.
- A conical vessel has base radius 31 cm and height 45 cm. Water is poured into the vessel until it is $\frac{2}{3}$ full. Find the volume (in cm³) of water in the vessel.
- A solid metallic sphere of radius 10 cm is melted and recast into 125 identical spheres. What is the ratio of the surface area of the original sphere to the total surface area of 6 smaller spheres so formed?
- Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm. Use $\pi = \frac{22}{7}$
- The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer) (Use $\pi = \frac{22}{7}$)
