# Tips And Tricks And Shortcuts on Perimeter Area Volume Questions

## Tips And Tricks And Shortcuts on Perimeter Area Volume:-

Here, are quick and easy tips and tricks for you on Perimeter, Area, and Volume. Learn, the tricks and concept on Perimeter, area and volume.

## Type 1: Find the area, perimeter, length, breadth and some other sides of the shapes

### 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 = 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

## Find the volume & surface area

### Question 1

What is the total surface area of a right circular cone of height 10 cm and base radius 7 cm?

Options:

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 = √h2 + r2
l = √100+49 = √149= 12.2
Total surface area of cone = πrl + πr²
22/7 * 7 * 12.2 + 22/ 7 * 7 * 7
268.4 + 154
422.4 cm²

## Percentage increase or decrease

### 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. 20% increase
D. 20% decrease

#### Solution:

Original area = l * b
New length = 50% increase = 150/100l = 3/2l
New breadth = 20% decrease = 80/100b = 4/5b
Therefore, new area = 3/2l * 4/5b
New area = 6/5lb
Change in Area = New Area – Original Area
Change in Area = 6/5lb – lb
Change in Area = 1/5lb
Percentage change in area = 1/5lb/ lb * 100
Percentage change in area = 1/5 * 100 = 100/5 = 20%
Since, the answer is positive, it means there is increase in the area.

## Type 4: Find cost

### 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?

Options:

A. Rs. 400
B. Rs. 420
C. Rs. 540
D. Rs. 450

#### Solution:

Area of trapezium = 1/2* (sum of parallel sides) * distance between them
Area of trapezium = 1/2 * (4 + 6) + 8
Area of trapezium = 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 