Question 1: The ratio between the length and the breadth of a rectangular plot is 6:4. Mily was cycling along the boundary of the plot at a speed of 10 km/hr. He completes one round of the plot in 12 minutes. Find the area of the plot?
Options
A. $240000 m^2$
B. $20000 m^2$
C. $24000 m^2$
D. $525000 m^2$
Solution :
Distance covered by Mily in 12 minutes = $\frac{10000}{60} × 12 = 2000 m$
Therefore, perimeter = 2000m
Length = 6x and breadth = 4x
Then 2 (l + b) = 2000
2 (6x + 4x) = 2000
2 (10x) = 2000
20x = 2000
x = 100
Length = 6x = 6 * 100 = 600
Breadth = 4x = 4 * 100 = 400
Therefore, Area $ = l * b = 600 * 400 = 240000 m^2 $
Correct option: A
Question 1 What is the total surface area of a right circular cone of height 10 cm and base radius 5 cm?
Options
A. $322.1 m^2$
B. $399.4 cm^2$
C. $402.5 cm^3$
D. $409.3 cm^2$
Solution :
h = 10 cm, r = 5 cm
Slant height $= l = \sqrt{h^2 + r^2 }$
$l = \sqrt{100 + 25 } = \sqrt{125 } = 11.18$
Total surface area of cone $ = πrl + πr^2$
$(\frac{22}{7} × 7 × 11.18)+ (\frac{22}{7} × 7 × 7 )$
245.96 + 154
$399.96 cm^2$
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?
Options
A. $70 % decrease$
B. $30 % increase$
C. $35 % increase$
D. $29 % decrease$
Solution :
Original area = l * b
New length = 50% increase $ = \frac{150}{100} l$
$ = \frac{3}{2} l$
New breadth = 20% decrease $ = \frac{80}{100} b = \frac{4}{5} b$
Therefore, new area $ = \frac{3}{2} l * \frac{4}{5} b$
New area $=\frac{6}{5} lb$
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} lb * 100$
Percentage change in area $ = \frac{1}{5} * 100 = \frac{100}{5} = 20%$
Since, the output is positive, it means there is increase in the area.
Correct option: C
Question 1 : A wall is of the form of a trapezium with height 4 m and parallel sides being 3 m and 5 m. What is the cost of painting the wall, if the rate of painting is Rs. 50 per square metre?
Options
A. Rs. 780
B. Rs. 920
C. Rs. 800
D. Rs. 750
Solution :
Given, height of trapezium = 3m, two sides length = 3m and = 5m.
Area of trapezium $ = \frac{1}{2} * (side_1 + side_2) \times height$
Area of wall $ = \frac{1}{2} * (5 + 3) \times 4$
$ \frac{1}{2} \times 8 \times 4 = 16^2 m $
Rate of painting per square meter is Rs.50
Therefore, to paint 16 square meter, total cost of painting = 16 * 50 = Rs. 800
Correct option: C