Question:
The volume of a cuboid is twice that of the volume of a cube. The dimensions of the cuboid are 9 cm, 8 cm, and 6 cm. If it costs ₹2.50 per sq.cm. for painting, the amount required to paint the surfaces of the cube (in rupees) is:
The volume of a cuboid is twice that of the volume of a cube. The dimensions of the cuboid are 9 cm, 8 cm, and 6 cm. If it costs ₹2.50 per sq.cm. for painting, the amount required to paint the surfaces of the cube (in rupees) is:
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If the volume of a cube is known, first find its side length by taking the cube root, then compute the surface area.
Updated On: Jun 12, 2026
- \(540\)
- \(520\)
- \(480\)
- \(440\)
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The Correct Option is A
Solution and Explanation
Step 1: Find volume of cuboid. \[ 9\times8\times6 = 432 \] cm\(^3\).
Step 2: Find volume of cube. Given cuboid volume is twice cube volume. \[ V_{\text{cube}} = \frac{432}{2} = 216 \] cm\(^3\).
Step 3: Determine side of cube. \[ a^3=216 \] \[ a=6 \] cm.
Step 4: Find total surface area. \[ 6a^2 = 6(6^2) = 216 \] sq. cm.
Step 5: Calculate painting cost. \[ 216\times2.5 = 540 \] Therefore, \[ \boxed{540} \]
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