Perimeter can be thought of as the length of the outline of a shape.
Surface area is the area of the two-dimensional surface of a three-dimensional object.
Volume is the space that an object occupies.
1. The sides of a triangle are in the ratio $ \frac{1}{3}: \frac{1}{2} : \frac{1}{4} $ Find the smallest side of the triangle, if the perimeter of the triangle is 78 cm.
Options:
A. 20 cm
B. 24 cm
C. 36 cm
D. 18 cm
Solution:
According to the question, ratio of the side of the triangle are $\frac{1}{3}: \frac{1}{2} : \frac{1}{4} = 6:3:4 $
Perimeter of the triangle = 78 cm
Therefore 6x + 4x + 3x = 78
13x = 78
x = 6
The Sides are : 6 x 6 = 36 cm
6 x 4 = 24 cm
6 x 3 = 18 cm
Correct option: D
2. A rope makes 120 rounds of cylinder with base radius 10 cm. How many times it can go round a cylinder with base radius 20 cm?
Options:
A. 70 cm
B. 60 cm
C. 45 cm
D. 50 cm
Solution:
Le the round be a
If radius is more, then rounds will be less as the length of the ropes remains the same
x = 2*π*10*120…(1)
Similarly,
x = 2 * π * 20 * a…(2)
From (1) and (2)
10 * 120 = 20 * a
=> a = 60
Correct option: B
3. Find the area of a parallelogram with base 20 m and height 4 m.
Options:
A. 120 m²
B. 24 m²
C. 150 m²
D. 80 m²
Solution:
Area of parallelogram = b * h
Area of parallelogram = 20 * 4 = 80 m²
Correct Option: A
1. A cube of 5 cm was cut into as many 1 cm cubes as possible. Find out the ratio of the surface area of the larger cube to that of the surface areas of the smaller cubes?
Options:
A. 1:2
B. 2:3
C. 1:5
D. 1:3
Solution:
Volume of the original cube $ = 53 = 125 cm^3$.
Volume of each smaller cubes $ = 1 cm^3$. It means there are 125 smaller cubes.
Surface area of the cube $ = 6a^2$
Surface area of the larger cube = 6a2 = 6 * 52 = 6 * 25 = 150
Surface area of one smaller cubes = 6 (1²) = 6
Now, surface area of all 125 cubes = 125 * 6 = 750
Therefore,
Required ratio = Surface area of the larger cube: Surface area of smaller cubes = 150: 750
= 1: 5
Correct option: C
2. The curved surface area of a cylindrical pillar is 264 m² and its volume is 924m³. Find the ratio of its diameter to its height.
Options:
A. 7:4
B. 3:4
B. 6:5
B. 7:3
Solution:
Volume of cylinder $ = πr^2h$
Curved Surface area of cylinder = 2 πrh
$\frac{\text{Volume of cylinder}}{\text{Curved Surface area of cylinder}}$
$\frac{πr^2h}{2 πrh} = \frac{924}{264}$
$r = \frac{924}{264} \times 2$
r = 7
Curved Surface area of cylinder = 2πrh = 264
$ 2 \times \frac{22}{7} \times h = 264 $
$ h = 264 \frac{22}{7} \times \frac{1}{2} \times \frac{1}{7} $
h = 6
Now, required ratio $ = 2 \times \frac{r}{h} = 2 \times \frac{7}{6} = \frac{14}{6} = \frac{7}{3} = 7 : 3 $
Correct option: D
1. What will be the cost of gardening 1 metre broad boundary around a rectangular plot having a perimeter of 340 metres at the rate of Rs.10 per square metre?
Options:
A. Rs. 4356
B. Rs. 5660
C. Rs. 3440
D. Rs. 4040
Solution:
2(l+b) = 400 (given)
Area of the boundary = [(l+2) (b+2) -- lb] = 2 (l + b) + 4 = 404
∴ Cost of gardening = Rs. (404 × 10) = Rs. 4040
Correct option: B
2. What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ?
Options:
A. Rs. 3710
B. Rs. 3770
C. Rs. 3944
D. Rs. 3580
Solution:
Let the side of the square plot be 'a' ft.
Given area of the plot (a x a) = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 x 58 = Rs. 3944.
Correct option: C
3. A rectangular wall whose length is 10 m more than its breadth. The cost of painting the wall is at Rs 30 per meter is Rs. 1800, what is the length of the wall in meters?
Options:
A. 18.5m
B. 27.5 m
C. 25 m
D. 20 m
Solution:
Breadth of the wall = x
Length of the wall = x + 10
Perimeter of the rectangular wall $ = \frac{1800}{30} = 60m $
2 (l+b) = 60
2 (x + 10 + x) = 60
2 (2x + 10) = 60
2x + 10 = 30
2x = 20
x = 10
Length = x + 10 = 10 + 10 = 20 m
Correct Option: D