Surface Areas And Volumes Of Solid Figures
NIOS · Class 10 · Maths
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See them allSolve: A cuboid has length 4 cm, breadth 3 cm, and height 12 cm. Find its surface area.
Answer
Step 1: Use surface area of cuboid = 2(lb + bh + hl). Step 2: Substitute values = 2(4×3 + 3×12 + 12×4). Step 3: = 2(12 + 36 + 48) = 2×96. Answer: 192 cm².
Solve: A cuboid has length 4 cm, breadth 3 cm, and height 12 cm. Find its volume.
Answer
Step 1: Use volume of cuboid = lbh. Step 2: Substitute values = 4×3×12. Step 3: = 144. Answer: 144 cm³.
Solve: Find the diagonal of a cuboid with l = 4 cm, b = 3 cm, h = 12 cm.
Answer
Step 1: Use diagonal of cuboid = √(l² + b² + h²). Step 2: Substitute = √(4² + 3² + 12²). Step 3: = √(16 + 9 + 144) = √169. Step 4: √169 = 13. Answer: 13 cm.
Solve: A cube has edge 13 cm. Find its surface area.
Answer
Step 1: Use surface area of cube = 6a². Step 2: Substitute a = 13 cm. Step 3: = 6×13² = 6×169. Step 4: = 1014. Answer: 1014 cm².
Solve: A cube has volume 2197 cm³. Find its edge and diagonal.
Answer
Step 1: Use volume of cube = a³. Step 2: a³ = 2197 = 13³, so a = 13 cm. Step 3: Use diagonal of cube = a√3. Step 4: Diagonal = 13√3 cm. Answer: Edge = 13 cm, diagonal = 13√3 cm.
When do you use the formula 2(lb + bh + hl)? Give a solved example.
Answer
Use it for the surface area of a cuboid. Example: l = 6 m, b = 3 m, h = 2.5 m. Step 1: 2(lb + bh + hl) Step 2: = 2(6×3 + 3×2.5 + 2.5×6) Step 3: = 2(18 + 7.5 + 15) = 2×40.5 Answer: 81 m².
A cuboidal tank is 5 m long and 4 m wide and contains 60 m³ of water. Find its depth.
Answer
Step 1: Use volume of cuboid = lbh. Step 2: Let depth = d. Step 3: 5×4×d = 60. Step 4: 20d = 60. Step 5: d = 60/20 = 3. Answer: 3 m.
A wooden box is 1.5 m long, 1.25 m broad, 65 cm deep, and open at the top. Find the area of wood used.
Answer
Step 1: Convert depth: 65 cm = 65/100 m = 0.65 m. Step 2: For an open-top box, area = lb + 2bh + 2hl. Step 3: = 1.5×1.25 + 2×1.25×0.65 + 2×0.65×1.5 Step 4: = 1.875 + 1.625 + 1.95 Step 5: = 5.45. Answe…
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