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Long Answer Type

41. Two cubes each with side b are joined to form a cuboid figure. What is the surface area of this cuboid? Is it 12b²? Is the surface area of cuboid formed by joining three such cubes, 18b²? why?

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42. How will you arrange 12 cubes of equal length to form a cuboid of smallest surface area?

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Short Answer Type

43.

After the surface area of a cube is painted the cube is cut into 64 smaller cubes of same dimensions. How many have no face painted? 1 face painted? 2 faces painted? 3 faces painted?

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44. Find total surface area of the following cylinders.

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45.

Note that lateral surface area of a cylinder is the circumference of base x height of cylinder. Can we write lateral surface area of a cuboid as perimeter of base x height of cuboid?

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46. There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

Total surface area of the cuboid (a) = 2[lb + bh + hl]
= 2 [(60 x 40) + (40 x 50) + (50 x 60)] cm²
= 2[2400 + 2000 + 3000] cm²
= 2[7400 cm²] = 14800 cm²
Total surface area of the cuboid (b) = 2[lb + hh + hl]
= 2[(50 x 50) + (50 x 50) + (50 x 50)]
= 2[2500 + 2500 + 2500] cm²
= 2 [ 7500 cm²] = 15000 cm²
Since the total surface area of the second (b) is true.
∴ Cuboid (a) will require lesser material.

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47. A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?

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48. Find the side of a cube whose surface area is 600 cm².

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49. Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except bottom of the cabinet.

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50. Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m² of area is painted. How many cans of paint will she need to paint the room ?

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