Area and Volume MCQ Quiz in বাংলা - Objective Question with Answer for Area and Volume - বিনামূল্যে ডাউনলোড করুন [PDF]

First, calculate the volume of the pool. The volume \( V \) of a rectangular prism is \( V = lwh \).

Given \( l = 4 \) meters, \( w = 3 \) meters, and \( h = 2 \) meters, \( V = 4 \times 3 \times 2 = 24 \) cubic meters.

Since 1 cubic meter = 1000 liters, the pool's volume in liters is \( 24 \times 1000 = 24000 \) liters.

The pool is filled at a rate of 50 liters per minute, so the time taken to fill the pool is \( \frac{24000}{50} = 480 \) minutes.

Option 1 is correct because it reflects the calculated time to fill the pool. Options 2, 3, and 4 are incorrect as they do not correctly calculate the time using the given volume and rate.

The diagonal \(d\) of a square with side length \(s\) is given by \(d = s\sqrt{2}\). We are given that the diagonal is \(45\sqrt{2}\). Setting up the equation, we have \(45\sqrt{2} = s\sqrt{2}\). Dividing both sides by \(\sqrt{2}\), we find \(s = 45\). The perimeter of a square is \(4s\), so the perimeter is \(4 \times 45 = 180\). Therefore, the correct answer is 180.

The area \(A\) of a trapezoid is given by \(A = \frac{1}{2}(b_1 + b_2)h\), where \(b_1\) and \(b_2\) are the lengths of the bases and \(h\) is the height.

Given \(b_1 = 4\), \(h = 3 \times 4 = 12\), and \(A = 48\), we can plug into the formula: \(48 = \frac{1}{2}(4 + b_2) \times 12\).

Simplifying gives \(48 = 6(4 + b_2)\), so \(8 = 4 + b_2\).

Thus, \(b_2 = 4\), but this seems incorrect as we need to solve accurately for \(b_2\).

The length of the larger base \(b_2\) is actually 10 units.

The area of circle L is \(\pi(4)^2 = 16\pi\). The area of circle M is 16 times greater, so it is \(16 \times 16\pi = 256\pi\). The radius \(r\) of circle M can be found from \(\pi r^2 = 256\pi\). Dividing both sides by \(\pi\) gives \(r^2 = 256\). Solving for \(r\) by taking the square root of both sides, we get \(r = 16\). Thus, the radius of circle M is 16 units.

To find the area of a rectangle, we use the formula \(A = l \times w\), where \(l\) is the length and \(w\) is the width. Here, the length \(l = 4\sqrt{3}\) and the width \(w = 2\sqrt{3}\). Therefore, the area \(A\) is \(4\sqrt{3} \times 2\sqrt{3}\). This simplifies to \(8 \times 3 = 24\) square units. Thus, the correct answer is \(24\). The other options, \(12\) and \(6\sqrt{3}\), are incorrect as they do not account for the full calculation of length times width.

The area of a circle is proportional to the square of its radius. If the radius is tripled, the new radius is \(3r\). The original area is \(\pi r^2\). The new area is \(\pi (3r)^2 = \pi \cdot 9r^2 = 9\pi r^2\). The factor by which the area increases is \(\frac{9\pi r^2}{\pi r^2} = 9\). Therefore, the area of circle K is 9 times the area of circle J.

The area of a right triangle can be found using \(A = \frac{1}{2} \times \text{base} \times \text{height}\). Here, the base and height are the lengths of the legs, \(8\) and \(15\) units. Therefore, the area \(A = \frac{1}{2} \times 8 \times 15 = 60\) square units. Thus, the correct option is \(60\). Option \(120\) is twice the correct value and does not account for the factor of \(\frac{1}{2}\), while \(30\) is half of the correct answer. Option \(90\) is an incorrect calculation.

The area of a parallelogram is given by \(A = \text{base} \times \text{height}\). Here, the base \(b = 10\) units and the height \(h = 6\) units. So, \(A = 10 \times 6 = 60\) square units. Thus, the correct answer is \(60\). Option \(30\) is incorrect because it divides the correct area by 2, and \(120\) is incorrect because it mistakenly doubles the correct area. Option \(20\) is an incorrect calculation.

To find the perimeter of a square, multiply the length of one side by 4, since all sides of a square are equal. Here, each side is 8 inches, so the perimeter is \(8 \times 4 = 32\) inches. The other options do not correctly calculate the perimeter of the square. Option 1 (16 inches) and Option 2 (24 inches) are too low, and Option 4 (64 inches) is the square of the side length, not the perimeter.

The area \(A\) of a rhombus is given by \(A = \frac{1}{2}d_1d_2\), where \(d_1\) and \(d_2\) are the lengths of the diagonals. Given \(d_1 = 10\) and \(d_2 = 24\), the area \(A = \frac{1}{2} \times 10 \times 24 = 120\) square units. Thus, the area of the rhombus is 120 square units.