Test: Mensuration - 2 - JAMB MCQ

Let the width be x cm. Then the length is 2x cm. Perimeter = 2(x + 2x) = 36 cm. Solving for x, we get x = 6 cm. Hence, the area of the rectangle is 6 * (2 * 6) = 36 cm².

Circumference = 2πr. So, 44 = 2 * π * r. Solving for r, we get r = 7 cm. Length of the arc = (60/360) * 2 * π * 7 = 6 cm.

Perimeter of the sector = radius + radius + arc length = 12 + 12 + (120/360) * 2 * π * 12 = 56 cm.

Surface area of the cylinder = 2 * π * r * h = 2 * π * 7 * 14 = 616 cm². Surface area of the hemisphere = 2 * π * r² = 2 * π * 7² = 308 cm². Total surface area = 616 + 308 = 1156 cm².

If the difference in longitudes is 15°, the angle subtended at the center is also 15°. Using the formula distance = r * θ, we get 1000 = r * (15 * π / 180). Solving for r, we get r = 6400 km.

Area of the trapezoid = (1/2) * height * (sum of parallel sides) = (1/2) * 7 * (10 + x) = 105 cm². Solving for x, we get x = 20 cm.

Using the Pythagorean theorem, r² = (chord length/2)² + distance². So, r² = (16/2)² + 6². Solving for r, we get r = 10 cm.

Area of the sector = (1/2) * r² * θ = (1/2) * 10² * (θ * π / 180) = 25π cm². Solving for θ, we get θ = 90°.

Total surface area of the cone = πr(l + r) = π * 5 * (13 + 5) = 160π cm².

If the difference in latitudes is 30°, the angle subtended at the center is also 30°. Using the formula distance = r * θ, we get 1800 = r * (30 * π / 180). Solving for r, we get r = 3600 km.