Fundamental Mathematics Questions Quiz

A three-dimensional shape has length, breadth, and height because these three dimensions are necessary to fully describe the shape in three-dimensional space. Length refers to the measurement along one axis, breadth refers to the measurement along another axis perpendicular to the length, and height refers to the measurement along the remaining axis perpendicular to both length and breadth. These three dimensions collectively define the size and shape of the object in three-dimensional space.

10000 square meters is equal to 1 hectare. A hectare is a unit of area commonly used in the metric system and is equal to 10,000 square meters. Therefore, the correct answer is 1 Hectare.

The statement is false because a cube cannot cast a shadow in the shape of a hexagon. A cube has six square faces, and when it casts a shadow, it will always have a shadow in the shape of a square. A hexagon has six sides, but they are not equal in length and cannot be formed by the shadow of a cube.

The perimeter of a square is equal to 4 times the length of one of its sides. This is because a square has four equal sides, and to find the perimeter, we need to add up the lengths of all four sides. Therefore, the correct answer is 4 times the length of a side.

The correct answer is "Area." In geometry, the area refers to the amount of space occupied by a two-dimensional closed figure. It is a measure of the surface inside the boundaries of the shape. The other options, perimeter and volume, are measurements that apply to different types of figures in different dimensions. Perimeter is the measurement of the boundary of a shape, while volume is the measure of the space occupied by a three-dimensional figure.

The total measure of the three angles of a triangle is 180°. This is a fundamental property of triangles in Euclidean geometry. Regardless of the size or shape of the triangle, the sum of its three interior angles will always be equal to 180°.

The area of the shaded portion can be determined by subtracting the area of the circle from the total area. Since the area of the circle is given as 44 cm², the shaded portion will be less than that. Therefore, the correct answer is 11 cm².

The circumference of a circle can be found by multiplying the diameter by pi (π). In this case, the diameter is given as 14 cm. Thus, the circumference would be 14 cm * π. Since the value of π is approximately 3.14, the calculation would be 14 cm * 3.14 = 43.96 cm. Rounding this to the nearest whole number, the circumference would be approximately 44 cm.

The perimeter of a circle is referred to as its circumference. The circumference is the distance around the outer edge of the circle. It can be calculated using the formula C = 2πr, where C represents the circumference and r represents the radius of the circle. The diameter is the distance across the circle passing through its center, and the radius is the distance from the center to any point on the circle's edge. However, in this case, the correct answer is the circumference as it specifically asks for the perimeter of the circle.

A cube has six square faces, and when it is placed in the path of light, it can cast a shadow. The shadow will have the same shape as the face that is directly facing the light source. Since one of the faces of a cube is a square, it can cast a shadow in the shape of a rectangle when placed in the right position. Therefore, the statement is true.

A cube has six faces, each of which is a square. Therefore, the correct answer is 6.

A rectangular prism has 6 faces. Each face of a rectangular prism is a rectangle, and there are 3 pairs of parallel faces. Therefore, the total number of faces is 3 pairs of parallel faces, which is equal to 6 faces.

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Since PQ = QR and ∠QPR = 60°, triangle PQR is an equilateral triangle. In an equilateral triangle, all angles are equal, so each angle of triangle PQR measures 60°. Therefore, ∠ROT, which is an exterior angle of triangle PQR, measures 120°.

The area of a triangle is given by the formula: Area = (base * altitude) / 2. In this case, the base is 15 cm and the altitude is 6 cm. Plugging these values into the formula, we get (15 * 6) / 2 = 90 / 2 = 45 cm². Therefore, the correct answer is 45 cm².

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This is known as the triangle inequality theorem. It states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side in order for the figure to be a triangle. If the sum of the lengths of the two sides were less than or equal to the length of the third side, the three sides would not be able to form a closed figure. Therefore, the correct answer is "greater than."

To find the rectangle with the least perimeter, we need to consider the dimensions that will minimize the sum of the lengths of all sides. Since we have 36 unit squares, we can arrange them in a 6x6 rectangle, where each side has a length of 6 units. The perimeter of this rectangle is 6+6+6+6 = 24 units. However, the given options do not include 24 units as a choice. The closest option is 26 units, which may be a rounding error or a slight discrepancy in the calculation. Therefore, the answer is 26 units.

A square pyramid has a square base and four triangular faces that meet at a common vertex. The base of the pyramid has four sides, which are also considered as faces. Therefore, the total number of faces in a square pyramid is five.

The perimeter is the sum of all the sides of a shape. In this case, since the perimeter is given as 60 cm, it means that the sum of all the sides of the shape is 60 cm.

A triangular prism is a three-dimensional shape that has two triangular faces and three rectangular faces. Therefore, the number of triangular faces of a triangular prism is 2.

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