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1.  

Directions (Q 40–43): A garden is a 28 m × 14 m rectangle with a semicircle of diameter 14 m on each of its two shorter sides (see the figure). A circular pond of radius 3.5 m is dug inside the garden. (Take π = 22/7.)
garden

What is the total area of the garden (including the pond)?

Correct Answer: D [546 m²]

Explanation:

28 × 14 + two semicircles of r = 7 (one circle, 154) = 546 m².

2.  
(Use the directions above – Mensuration (2D & 3D), Q 40–43)
What is the length of the outer boundary of the garden?

Correct Answer: E [100 m]

Explanation:

Two 28 m sides + two semicircular arcs (one circumference 44) = 100 m.

3.  
(Use the directions above – Mensuration (2D & 3D), Q 40–43)
What is the cost of fencing the outer boundary at ₹ 45 per metre?

Correct Answer: B [₹ 4,500]

Explanation:

100 m × 45 = ₹ 4,500.

4.  
(Use the directions above – Mensuration (2D & 3D), Q 40–43)
What is the area of the garden excluding the pond?

Correct Answer: D [507.5 m²]

Explanation:

546 − 38.5 = 507.5 m².

5.  
From each corner of a square plate of side 14 cm, a quarter-circle of radius 7 cm is cut off. The area of the remaining plate is:

Correct Answer: A [42 cm²]

Explanation:

Four quarter-circles = one circle of r = 7 (154) → 196 − 154 = 42 cm².

6.  
A solid is made of a cylinder of radius 7 cm and height 14 cm with a hemisphere of radius 7 cm on its top. Its total surface area is:

Correct Answer: B [1,078 cm²]

Explanation:

Base 154 + cylinder side 2πrh = 616 + hemisphere 2πr² = 308 → 1,078 cm².

7.  
A solid is a cylinder of radius 7 cm and height 9 cm with a cone of the same radius and height 12 cm on top. Its volume is:

Correct Answer: C [2,002 cm³]

Explanation:

Base 154 × (9 + 12/3) = 154 × 13 = 2,002 cm³.

8.  
Quantity I: Volume of a cone of radius 6 cm and height 8 cm.
Quantity II: Volume of a hemisphere of radius 6 cm.

Correct Answer: B [Quantity I < Quantity II]

Explanation:

I: ⅓π × 36 × 8 = 96π. II: ⅔π × 216 = 144π.

9.  
What is the area of the rectangle?
I. Its diagonal is 25 m.
II. Its perimeter is 62 m.

Correct Answer: D [Both statements together are needed]

Explanation:

Together: l + b = 31, l² + b² = 625 → 2lb = 961 − 625 → lb = 168 m².

10.  
A right triangle has hypotenuse 13 cm and area 30 cm².
Quantity I: The length (cm) of one of its two shorter sides (either one).
Quantity II: 5

Correct Answer: C [Quantity I ≥ Quantity II]

Explanation:

Legs a, b: a² + b² = 169, ab = 60 → legs are 5 and 12.

11.  
A running track has two straight parallel stretches of 100 m and two semicircular ends. The inner semicircles have radius 35 m and the track is 7 m wide. The area of the track is:

Correct Answer: E [3,094 m²]

Explanation:

Straights 2 × 100 × 7 = 1,400; ends make a ring π(42² − 35²) = 1,694 → 3,094 m².

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