Geometric Shapes and Mensuration Flashcards

A piece of farmland is in the shape of a trapezium. Its parallel sides are 15 m and 25 m long. If the perpendicular distance between the parallel sides is 10 m, what is the area of the farmland?

Answer: 200 m²

The formula for the area of a trapezium is A = 1/2 * (a+b) * h, where 'a' and 'b' are the lengths of the parallel sides and 'h' is the height. Substituting the given values: A = 1/2 * (15 + 25) * 10 = 1/2 * (40) * 10 = 20 * 10 = 200 m².

A cylindrical water tank has a radius of 7 metres and a height of 5 metres. Calculate the maximum volume of water the tank can hold. (Take π = 22/7)

Answer: 770 m³

The formula for the volume of a cylinder is V = πr²h. Given r = 7 m and h = 5 m, we substitute these values into the formula: V = (22/7) * (7)² * 5 = (22/7) * 49 * 5. The 7 in the denominator cancels out with 49 to leave 7. So, V = 22 * 7 * 5 = 154 * 5 = 770 m³.

The circumference of a circular running track is 440 metres. What is the area of the field enclosed by the track? (Take π = 22/7)

Answer: 15,400 m²

First, find the radius (r) using the circumference formula, C = 2πr. So, 440 = 2 * (22/7) * r, which simplifies to 440 = (44/7) * r. To find r, calculate r = (440 * 7) / 44 = 10 * 7 = 70 m. Now, use the radius to find the area with the formula A = πr². A = (22/7) * (70)² = (22/7) * 4900. This calculates to 22 * 700 = 15,400 m².

A 13-metre-long ladder is placed against a vertical wall. The foot of the ladder is 5 metres away from the base of the wall. How high up the wall does the ladder reach?

Answer: 12 m

This scenario forms a right-angled triangle with the ladder as the hypotenuse (c=13m), the distance from the wall as one side (b=5m), and the height on the wall as the other side (a). Using Pythagoras' theorem (a² + b² = c²), we have a² + 5² = 13². This gives a² + 25 = 169. So, a² = 169 - 25 = 144. Therefore, a = √144 = 12 metres.

Which of the following statements correctly describes the properties of a cuboid?

Answer: It has 8 vertices, 12 edges, and 6 faces.

A cuboid is a three-dimensional shape with 8 corners (vertices), 12 straight lines (edges), and 6 flat surfaces (faces).

A sugar cube has an edge length of 2 cm. What is the total surface area of the cube?

Answer: 24 cm²

A cube has 6 identical square faces. The area of one face is length × length, which is 2 cm * 2 cm = 4 cm². The total surface area is the area of one face multiplied by the number of faces (6). So, Total Surface Area = 6 * (side length)² = 6 * (2)² = 6 * 4 = 24 cm².