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August 12, 2023
The area is the space occupied by a shape of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure, and Volume is calculated by the quantity of three-dimensional space enclosed by a closed surface.
Question 1: The ratio between the length and the breadth of a rectangular plot is 7:3. Rahul was cycling along the boundary of the plot at a speed of 10 km/hr. He completes one round of the plot in 6 minutes. Find the area of the plot?
Options:
A. 52000 m²
B. 51500 m²
C. 53500 m²
D. 52500 m²
Solution: Distance covered by Rahul in 6 minutes = \frac{10000}{60} × 6 = 1000 m
Therefore, perimeter = 1000m
Length = 7x and breadth = 3x
Then 2 (l +b) = 1000
2 (7x + 3x) = 1000
2 (10x) = 1000
20x = 1000
x = 50
Length = 7x = 7 * 50 = 350
Breadth = 3x = 3 * 50 = 150
Therefore, Area = l * b = 350 * 150 = 52500 m²
Correct option: D
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Question 1 What is the total surface area of a right circular cone of height 10 cm and base radius 7 cm?
A. 422.4 m²
B. 422.4 cm²
C. 422.4 cm³
D. 422.4 cm
Solution: h = 10 cm, r = 7 cm
Slant height = l = \sqrt{h^2 + r^2 }
l = \sqrt{100 + 49 } = \sqrt{149 }= 12.2
Total surface area of cone = πrl + πr²
(\frac{22}{7} × 7 × 12.2 )+ (\frac{22}{7} × 7 × 7 )
268.4 + 154
422.4 cm²
Correct option: B
Question 1:If length of the rectangle is increased by 50% and breadth is decreased by 20%. Then what is the percentage change in the area?
A. 70% decrease
B. 30 % increase
C. 20% increase
D. 20% decrease
Solution: Original area = l * b
New length = 50% increase = \frac{150}{100}l
= \frac{3}{2}lNew breadth = 20% decrease = \frac{80}{100}b = \frac{4}{5}b
Therefore, new area = \frac{3}{2}l * \frac{4}{5}b
New area =\frac{6}{5} l b
Change in Area = New Area – Original Area
Change in Area = \frac{6}{5}lb – lb
Change in Area = \frac{1}{5}lb
Percentage change in area = \frac{\frac{1}{5}lb}{lb} * 100
Percentage change in area = \frac{1}{5} * 100 = \frac{100}{5} = 20%
Since, the answer is positive, it means there is increase in the area.
Correct option: C
Question 1 A wall of trapezium shape has height 8 m. The parallel sides of trapezium are 4 m and 6 m. If the rate of painting per square meter is Rs.50 than find the cost painting the complete wall?
A. Rs. 400
B. Rs. 420
C. Rs. 540
D. Rs. 450
Solution: Area of trapezium =\frac{1}{2} * (sum of parallel sides) * distance between them
Area of trapezium = \frac{1}{2} * (4 + 6) + 8
Area of trapezium = \frac{1}{2} * (18)
Area of trapezium = 9 square meter
Rate of painting per square meter is Rs.50
Therefore, to paint 9 square meter, total cost of painting = 9 * 50 = Rs. 450
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