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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?

When 2 cubes are joined end to end:
Length (L) = b + b = 2b
Breadth (B) = b
Height (H) = b (∵ Height and breadth do not change)
∴ Total surface area = 2[LB + BH + HL]
= 2[(2b x b) + (b x b) + (b x 2b)]
= 2[2b² + b² + 2b²]
= 2[5b²]
= 10b²
∴ The total surface area is not 12b².

When 3 cubes are joined end to end:
Length (L) = 3b
Breadth (B) = b
Height (H) = b (Here too breadth and height do not change.)
∴ Total surface area of the cuboid = 2[LB + BH + HL]
= 2[(3b x b) + (b x b) + (b x 3b)]
= 2[3b²+b²+3b²]
= 2[7b²]
= 14b²
∴ The surface area is not 18b².

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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?

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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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