Area — Practice

Question 1

Find area of a triangle with base 10 cm and height 7 cm.

Accepted Answer

✦ Answer: A = (1/2) × 10 × 7 = 35 cm².

Question 2

Find area of circle with radius 21 cm. (π = 22/7)

Accepted Answer

✦ Answer: A = πr² = (22/7) × 21² = (22/7) × 441 = 1386 cm².

Question 3

A field is in the shape of a rectangle (length 30 m, breadth 20 m) with a semicircular extension at one end (radius = 10 m). Find the total area.

Accepted Answer

Step 1 — Rectangle area.
  A₁ = 30 × 20 = 600 m²

Step 2 — Semicircle area.
  Full circle area = π × 10² = 100π = 100 × 22/7 = 314.29 m² (approx)
  Semicircle = 314.29/2 = 157.14 m²

Step 3 — Total.
  Total = 600 + 157.14 = 757.14 m²

✦ Answer: Total area ≈ 757.14 m² (or 600 + 50π m² in exact form).

Question 4

A cylindrical tank has radius 7 m and height 10 m. (a) Find its volume. (b) Find the area to be painted on its curved surface (use π = 22/7).

Accepted Answer

Step 1 — Volume.
  V = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 1540 m³

Step 2 — Curved surface area (for painting).
  CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 m²

✦ Answer: (a) Volume = 1540 m³. (b) Curved surface area for painting = 440 m².

Question 5

A swimming pool is 25 m long, 10 m wide, and 1.5 m deep. (a) Find its volume in cubic metres. (b) How much water (in litres) is needed to fill it to the top? (c) Find the surface area of the walls and floor (NOT including the top open surface). (1 m³ = 1000 L).

Accepted Answer

Part (a) — Volume.
  V = L × B × H = 25 × 10 × 1.5 = 375 m³

Part (b) — Litres of water.
  V in L = 375 × 1000 = 3,75,000 litres

Part (c) — Surface area (walls and floor, not top).
  Floor area = L × B = 25 × 10 = 250 m²
  Walls:
    Two longer walls = 2 × (L × H) = 2 × (25 × 1.5) = 75 m²
    Two shorter walls = 2 × (B × H) = 2 × (10 × 1.5) = 30 m²
  Total walls = 75 + 30 = 105 m²
  Total (walls + floor) = 250 + 105 = 355 m²

✦ Answer: (a) Volume = 375 m³. (b) Water needed = 3,75,000 litres. (c) Surface area to tile = 355 m² (floor + 4 walls, no top).

Practice — Area

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