Test: Mensuration - 1 - JAMB MCQ

The length of an arc is given by (θ/360) × 2πr, where θ is the angle in degrees and r is the radius of the circle. Substituting the values, we get (60/360) × 2π × 6 = 6π cm.

 Let the width of the rectangle be x cm. The length is then 2x cm. The perimeter is given by 2(x + 2x) = 30 cm. Solving for x, we get x = 5 cm. Therefore, the length is 2(5) = 10 cm. The area is given by length × width = 10 cm × 5 cm = 50 cm².

The circumference of a circle is given by 2πr, where r is the radius. Solving the equation 2πr = 36π, we find r = 6 cm.

Let the width of the field be x m. The length is then x + 40 m. The area is given by length × width = (x + 40) m × x m = 2400 m². Solving for x, we get x = 30 m. Therefore, the length is x + 40 = 30 m + 40 m = 70 m.

The area of a sector is given by (θ/360) × πr², where θ is the angle in degrees and r is the radius of the circle. Substituting the values, we get (20/360) × π × 5² = 25π cm².

The volume of a cone is given by (1/3) × πr²h, where r is the radius of the base and h is the height. The height can be found using the Pythagorean theorem: h² = slant height² - radius² = 10² - 6² = 64. Therefore, h = √64 = 8 cm. Substituting the values, we get (1/3) × π × 6² × 8 = 120π cm³.

Let the width of the rectangle be x cm. The length is then 3x cm. The perimeter is given by 2(x + 3x) = 64 cm. Solving for x, we get x = 8 cm. Therefore, the length is 3(8) = 24 cm. The area is given by length × width = 24 cm × 8 cm = 192 cm².

The surface area of a cube is given by 6s², where s is the length of one of its edges. Solving the equation 6s² = 96, we find s = 4 cm. Therefore, the length of one of its edges is 4 cm.

The volume of a sphere is given by (4/3) × πr³, where r is the radius. Solving the equation (4/3) × πr³ = 288π, we find r = 6 cm.

The distance covered along a latitude is given by (θ/360) × circumference of the Earth, where θ is the angle in degrees and the circumference of the Earth is approximately 40,075 km. Substituting the values, we get (30/360) × 40,075 km = 4,008 km.