Mensuration
- The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 kmph completes one round in 8 minutes, then the area of the park is equal to
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Length of park = 3x metre (let)
Breadth = 2x metre
Perimeter of park = Distance covered by cyclist= 12 × 8 = 8 km 60 5 = 
8 × 1000 
metre 5
= 1600 metre
According to the question, 2 (3x + 2x) = 1600⇒ 10x = 1600 ⇒ x = 1600 = 160 10
∴ Area of the park = 3x × 2x = 6x² = 6 × (160)² = 153600 sq. metreCorrect Option: C
Length of park = 3x metre (let)
Breadth = 2x metre
Perimeter of park = Distance covered by cyclist= 12 × 8 = 8 km 60 5 = 8 × 1000 metre 5
= 1600 metre
According to the question, 2 (3x + 2x) = 1600⇒ 10x = 1600 ⇒ x = 1600 = 160 10
∴ Area of the park = 3x × 2x = 6x² = 6 × (160)² = 153600 sq. metre
- The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks measuring 22.5 cm by 10 cm by 7.5 cm can be painted out of this container?
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Whole surface area of a brick = 2 (l × b + b × h + h × l)
= 2 (22.5 × 10 + 10 × 7.5 + 7.5 × 22.5)
= 2 (225 + 75 + 0.75 × 225)
= 2 × 75 (3 + 1 + 0.75 × 3)
= 150 × 6.25 = 937.5 sq. cm.∴ Number of bricks = 9.3755 × 100 × 100 = 100 937.5 Correct Option: D
Whole surface area of a brick = 2 (l × b + b × h + h × l)
= 2 (22.5 × 10 + 10 × 7.5 + 7.5 × 22.5)
= 2 (225 + 75 + 0.75 × 225)
= 2 × 75 (3 + 1 + 0.75 × 3)
= 150 × 6.25 = 937.5 sq. cm.∴ Number of bricks = 9.3755 × 100 × 100 = 100 937.5
- 5 persons will live in a tent. If each person requires 16 m² of floor area and 100 m³ space for air then the height of the cone of smallest size to accommodate these persons would be
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Let the radius of the base of conical tent be r metre and its height be h metre.
∴ Area of base = πr² = 16 × 5 = 80 ......(i)Volume = 1 πr²h 3
= 5 × 100 cu. metre ......(ii)
On dividing equation (ii) by (i),= 1 πr²h = 5 × 100 3 πr² 80 ⇒ h = 75 = 18.75 metre 4 Correct Option: D
Let the radius of the base of conical tent be r metre and its height be h metre.
∴ Area of base = πr² = 16 × 5 = 80 ......(i)Volume = 1 πr²h 3
= 5 × 100 cu. metre ......(ii)
On dividing equation (ii) by (i),= 1 πr²h = 5 × 100 3 πr² 80 ⇒ h = 75 = 18.75 metre 4
- The length of canvas, 75 cm wide required to build a conical tent of height 14m and the floor area 346.5 m² is
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Area of the base of conical tent = 346.5 sq. metre
∴ πr² = 346.5⇒ 22 × r² = 346.5 7 ⇒ r² = 346.5 × 7 = 110.25 22
⇒ r = √110.25 = 10.5 metre
∴ Slant height = √h² + r²
= √(14)² + (10.5)² = √196 + 110.25
= √306.25 = 17.5 metre
∴ Area of curved surface of the tent = πrl= 22 × 10.5 × 17.5 7
= 577.5 sq. metre∴ Length of canvas = 577.5 = 577.5 × 100 75 75 100 = 57750 = 770 metre 75 Correct Option: D
Area of the base of conical tent = 346.5 sq. metre
∴ πr² = 346.5⇒ 22 × r² = 346.5 7 ⇒ r² = 346.5 × 7 = 110.25 22
⇒ r = √110.25 = 10.5 metre
∴ Slant height = √h² + r²
= √(14)² + (10.5)² = √196 + 110.25
= √306.25 = 17.5 metre
∴ Area of curved surface of the tent = πrl= 22 × 10.5 × 17.5 7
= 577.5 sq. metre∴ Length of canvas = 577.5 = 577.5 × 100 75 75 100 = 57750 = 770 metre 75
- The number of paving stones each measuring 2.5m × 2m required to pave a rectangular courtyard 30m long and 17.5 m wide, is
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Number of paving stones = Area of courtyard Area of astone = 30 × 17.5 2.5 × 2
= 105Correct Option: D
Number of paving stones = Area of courtyard Area of astone = 30 × 17.5 2.5 × 2
= 105
