Explain these questions with diagram and images or figure if possible in the video and write all step by step solution of each question in simplest way for class 8 child..read image uploaded carefully for chapter fraction and decimals.of class 8 india,delhi.explain in best way---TOPIC : COMPARING QUANTITIES PERIMETER AND AREA CLASS – 8 1. What is 0.5% of 50 ? A) 250 B) 25 C) 2.5 D) 0.25 2. Urooj cycled along a straight road for 4400 m. The diameter of her bicycle’s tyre was 70 cm .How many rotations were made by her bicycles ? A) 10 B) 20 C) 1000 D) 2000 3. A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12cm .What is the difference between the areas ? A) 25cm² B) 20cm² C) 4 cm² D) 2 cm² 4. How many square strips having an area of 2 sq. cm will be required to cover the rectangular region shown here? (The strips can be cut if required, assume there is no wastage.) Chart/Diagram Description: Type: Geometric figure (rectangle with dimensions labeled) Main Elements: - A rectangle is shown. - The length of the rectangle is labeled as 22 cm. - The width (or height) of the rectangle is labeled as 8 cm. - The labels "8 cm" and "22 cm" are placed next to the respective sides. A) 30 B) 44 C) 88 D) 354 5. Five identical rectangular pieces of cloth of different prints when arranged as shown form a square patch. If the perimeter of each rectangular piece is 48 cm, what is the perimeter of the square patch? Chart/Diagram Description: Type: Arrangement of rectangles forming a square. Main Elements: - Five rectangular pieces are arranged side-by-side vertically to form a larger square shape. - Each rectangle has a different pattern (from left to right: hash symbols, solid yellow, small dots, crosses, stripes). - The arrangement forms a square patch overall. A) 240 cm B) 120 cm C) 96cm D) 80cm 1 6. Two identical triangular pieces of paper are pasted one on top of the other such that they overlap in a square of side 4 cm as shown below. Chart/Diagram Description: Type: Geometric figure (overlapping triangles and a square). Main Elements: - Two congruent right-angled triangles are shown overlapping. - The hypotenuse of one triangle runs from the bottom left upwards to the right. - The hypotenuse of the other triangle runs from the bottom right upwards to the left. - The triangles overlap in a square region in the center. - The side length of the square overlap region is labeled as 4 cm. - The base of each triangle outside the overlap square is shown. The length from the leftmost point to the start of the square is labeled as 8 cm. This likely represents the base of the non-overlapping part of one triangle or half the base of the full triangle before overlap. Based on the diagram, 8 cm appears to be the length of the horizontal leg of one triangle outside the square. - The height of each triangle outside the overlap square is also shown. The height from the top vertex of the square to the top vertex of the composite shape (which is the top vertex of the triangles) is labeled as 6 cm. This likely represents the vertical leg of the non-overlapping part of one triangle or half the height of the full triangle before overlap. Based on the diagram, 6 cm appears to be the height of the non-overlapping part of one triangle. A) 136 cm² B) 120cm² C) 104 cm² D) 88 cm² 7. The cost price of 22 pens is selling price of 20 pens of same variety . Find the profit percentage . A) 10 % B) 15% C) 17.5% D) 20% 8. The length and breadth of a square are increased by 30% and 20% respectively .By what percentage the area of the rectangle so formed exceeds the area of the square ? A) 20 % B) 36% C) 50% D) 56 % 9. A circle is inscribed in a square of side 14m .The ratio of the area of the circle and that of the square is A) π : 3 B) π : 4 C) π : 2 D) π : 1 10. If the area and circumference of a circle are numerically equal, then diameter of the circle is A) Area B) Circumference C) 4 D) 2π 11. A person invests money in three different investments for 6 years, 10 years and 12 years at 10%, 12% and 15% simple interest per annum respectively . On maturity , he receives the same interest on each investment . What is the ratio of his investment ? A) 2:3:4 B) 6:3:2 C) 3:5:8 D) 2:3:5 **Question 12** **Question Stem:** 12. In the figure given below, O is the centre of the three circles, I ,II and III . The length of PQ is 20 cm and the diameter of the circle II is 12 cm. What will be the radius of the largest circle ? **Options:** A) 8 cm B) 10 cm C) 14cm D) 16cm **Chart/Diagram Description:** * **Type:** Geometric figure, showing three concentric circles. * **Main Elements:** * **Circles:** Three concentric circles labeled I (innermost), II (middle), and III (outermost). * **Point:** O is the center of all three circles. * **Line Segment:** A horizontal line segment passes through the center O. Points P and Q are on this line. * **Points on Line Segment:** P is on the outermost circle (III), and Q is on the middle circle (II). O is between P and Q. * **Labels:** Circles are labeled I, II, III. The center is labeled O. Points on the diameter are labeled P and Q. **Question 13** **Description:** 13. Rahul used 2 identical white squares and 8 identical grey squares to make the shapes below. **Question Stem:** What can we say about the perimeter of the two shapes? **Options:** A. The perimeter of Shape 2 is greater than that of Shape 1. B. The perimeter of Shape 1 is greater than that of Shape 2. C. The perimeters of both Shape 1 and Shape 2 are equal. D. (cannot be concluded without knowing the actual measures of the white and grey squares) **Chart/Diagram Description:** * **Type:** Arrangement of squares forming two shapes. * **Main Elements:** * Two shapes are shown side-by-side, labeled "Shape 1" and "Shape 2" below them. * **Shape 1:** Composed of one white square and four grey squares. The white square is in the center. Two grey squares are attached to the top edge of the white square, one on the left and one on the right, adjacent to each other. Two grey squares are attached to the bottom edge of the white square, one on the left and one on the right, adjacent to each other. All squares appear to be the same size. * **Shape 2:** Composed of one white square and four grey squares. The white square is in the center. One grey square is attached to the middle of the top edge of the white square. One grey square is attached to the middle of the bottom edge of the white square. One grey square is attached to the middle of the left edge of the white square. One grey square is attached to the middle of the right edge of the white square. All squares appear to be the same size. **Question 14** **Description:** 14. Shown below are three shapes. Shape 2 can be formed by arranging 2 triangles shown in shape 1. Shape 3 can be formed by arranging 3 triangles shown in shape 1. **Chart/Diagram Description (Initial Shapes):** * **Type:** Geometric shapes. * **Main Elements:** * Three shapes shown side-by-side, labeled "Shape 1", "Shape 2", and "Shape 3" below them. * **Shape 1:** A right-angled triangle. Appears to be an isosceles right-angled triangle. * **Shape 2:** A square. Formed by arranging two triangles like Shape 1. * **Shape 3:** A trapezoid/quadrilateral. Formed by arranging three triangles like Shape 1. **Description (New Shape):** A new shape is formed by arranging the above three shapes. **Chart/Diagram Description (New Shape):** * **Type:** Composite geometric shape. * **Main Elements:** * A larger shape is shown below the initial three shapes. * This shape is formed by combining Shape 1, Shape 2, and Shape 3. * Shape 3 (the trapezoid) forms the base. * Shape 1 (the triangle) is placed on the left side of Shape 3, with its hypotenuse along the slanted edge of the trapezoid. * Shape 2 (the square) is placed on the right side of Shape 3, attached to its vertical edge. **Question Stem:** The area of the new shape is _________. **Options:** A. thrice the area of shape 1 + twice the area of shape 2 B. twice the area of shape 1 + twice the area of shape 2 C. twice the area of shape 2 + thrice the area of shape 3 D. once the area of shape 1 + once the area of shape 2 + once the area of shape 3 **Question 15** **Question Stem:** 15. Simple interest on a certain amount is ( 9 / 16 ) of the principal . If the number representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is **Options:** A) 5 and ½ years B) 6 and ½ years C) 7 years D) 7 and ½ years