Explain these questions from que 6-11 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 and write all formulas or rules whereas required..read image uploaded carefully 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
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Let's solve Question 6 step by step. We have two identical triangles overlapping in a square of side 4 centimeters. Looking at the diagram, the base outside the square is 8 centimeters, and the height outside is 6 centimeters. So the total base is 8 plus 4 equals 12 centimeters, and total height is 6 plus 4 equals 10 centimeters. Each triangle has area one-half times 12 times 10 equals 60 square centimeters. The overlap square has area 4 times 4 equals 16 square centimeters. The total area is 60 plus 60 minus 16 equals 104 square centimeters. The answer is C.
Now let's solve Question 7 about profit percentage. The cost price of 22 pens equals the selling price of 20 pens. We set up the equation: 22 times cost price equals 20 times selling price. Rearranging, we get selling price over cost price equals 22 over 20, which simplifies to 11 over 10. This means if cost price is 10 units, selling price is 11 units. The profit is 11 minus 10 equals 1 unit. Profit percentage is profit over cost price times 100, which is 1 over 10 times 100 equals 10 percent. The answer is A.
Let's solve Question 8 about area increase. We start with a square of side s and area s squared. The length is increased by 30 percent, making it 1.3s. The breadth is increased by 20 percent, making it 1.2s. The new area becomes 1.3s times 1.2s, which equals 1.56 s squared. The increase in area is 1.56 s squared minus s squared, divided by s squared, times 100. This gives us 0.56 times 100 equals 56 percent increase. The answer is D.
Let's solve Question 9 about a circle inscribed in a square. When a circle is inscribed in a square of side 14 meters, the diameter of the circle equals the side of the square, which is 14 meters. So the radius is 14 divided by 2, equals 7 meters. The area of the circle is pi times radius squared, which is pi times 49, equals 49 pi square meters. The area of the square is 14 squared, equals 196 square meters. The ratio of circle area to square area is 49 pi to 196. Dividing both by 49, we get pi to 4. The answer is B.
Let's solve the final two questions. For Question 10, if area equals circumference numerically, we have pi r squared equals 2 pi r. Dividing by pi r, we get r equals 2, so diameter equals 4. The answer is C. For Question 11, using simple interest formula, the interests are 0.6 times P1, 1.2 times P2, and 1.8 times P3. Since all interests are equal, we get 0.6 P1 equals 1.2 P2 equals 1.8 P3. This gives us the ratio P1 to P2 to P3 equals 6 to 3 to 2. The answer is B.