Direct Variations

Q. The volume of a sphere is directly proportional to the cube of its radius. If the volumes of two spheres are in ratio $8:1$, what is the ratio of the radii of the spheres?

1. $2:1$
2. $1:2$
3. $1:4$

Q. Which of the following is true?

1. Y is directly proportional to X then, Y = k X, where k is a constant
2. Y is directly proportional to X then, Y = k X, where k is a variable
3. Y is indirectly proportional to X then, Y = k X, where k is a constant
4. Y is indirectly proportional to X then, Y = k X, where k is a variable

Q.

If Mohans income is $25\%$ more than Ramans income, then Ramans income is less than Mohans income by

1. $25\%$

2. $80\%$

3. $20\%$

4. $75\%$

Q. Weight of an object on Earth varies directly as the weight of the same object on the Moon. An object weighing 300 lbs on Earth weighs 48 lbs on the Moon. If an object weighs 65 lbs on Earth, then it will weigh lbs on Moon.

Q.

In a car factory, $6$ machines can make $6$ wheels in $6$ minutes.

How long will it take $30$ machines to make $30$ wheels?

Q.

What does proportional relationship mean in math?

Q. Weight of an object on Earth varies directly as the weight of the same object on the Moon. An object weighing 300 lbs on Earth weighs 48 lbs on the Moon. If an object weighs 65 lbs on Earth, then it will weigh lbs on Moon.

Q. Cows in a herd graze in the sun. To protect themselves from the sun, they apply sunscreen. 2 mL of sunscreen protects an area of $50{\text{cm}}^2$ of skin. If Daisy the cow, has to protect an area of $4000{\text{cm}}^2$ of her skin with sunscreen then amount of sunscreen she would need is

Q. Sam bakes delicious cakes. A specific cake recipe requires $1$ lb of flour. If he had $8$ oz of flour with him, then the additional amount(in pounds) of flour to be added according to the recipe is

Q. Olivia went to a shop to buy candies for her birthday celebration. The shopkeeper sells candies which follows a certain relationship with the price as follows: No. of Candies Price ($\$$)

2	8	18
1	2	3

Determine the number of candies Olivia will purchase with $\$$5.

1. 50

Q. Sam read 10 pages of a novel in 40 minutes. If he read for 2 hr and 40 min, how many pages of novel will he read? Given the speed of reading is same.

1. 39
2. 40
3. 41
4. 42

Q. The ratio of two directly proportional quantities is always .

1. a constant
2. a variable
3. zero

Q.

If the cost of $6$ cans of juice is $Rs180$, then:

Cost of ______ cans of juice is $Rs270$.

Q. Jack works in packaging at a candy factory, he can load 100 bags of candies in a box in 8 minutes, then the time taken for packing 550 candy bags is minutes

Q. Sam's bakery has 4 ovens which bake a total of 200 cookies daily. Each oven bakes equal number of cookies. He adds five more similar ovens to meet the increasing demand. The number of cookies that can be produced each day is .

Q.

For every 6 lbs of chocolate, 2 lbs of sugar is recquired as per the chocolate cake recipe. If you're going to use 60 lbs of chocolate in a batch, you'll need pounds of sugar.

Q. If y is directly proportional to x, then find a and b

x	6	12	18	a
y	5	10	15	b

1. a = 24, b = 20
2. a = 20, b = 24
3. a = 30, b = 20
4. a = 30, b = 25

Q. The rise in population of a country varies directly with each passing year.
The population has risen by 2 million in past 5 years. Calculate the population rise in next 10 years?

1. 4 million
2. 5 million
3. 6 million
4. 7 million

Q.

Fill in the following blanks.

$\frac{15}{18}=\frac{▫}{6}=\frac{10}{▫}=\frac{▫}{30}$

Q. $P$ varies directly as cube of $r$. $P=26$ when $r=2$. When $r=4,P$ equals

1. 208

Q. Every single day a power plant supplies 40 MW electricity to 50 homes. Assuming each home consumes same amount of electricity, the total amount of electricity that will be supplied by the power plant when the number of homes is increased to 80 is

Q. If $x$ is in direct proportion to $y$ and at $x=10$, $y=5$, then the constant of proportionality is

1. 2
2. 1
3. 5

Q. If the cost of tickets for 30 students on a school trip to a nearby museum is 180 dollars, the cost of tickets for 100 students would be

1. 600

Q. A pipe can fill a tank of 100 liter in 2 hours. How many pipes are required to fill a bigger tank of 500 liter in 2 hours at the same rate?

1. 4
2. 5
3. 7
4. 5

Q.

The high school baseball team has won four of its last five games under Mark's leadership. How many games would the team have to play in order to win 20 games if they keep winning at the same rate?

1. 16
2. 25
3. 24
4. 20

Q. For a dollar, if you can get 3 candies, then the total money spent and total number of candies are proportional.

1. directly
2. not proportional
3. Can't determine

Q. If the dimensions of rectangle are $"l"\&"b"$ and $"a"$ is its area, then for the ratio $\frac{a}{lb}$, the constant of proportionality is .

1. 2
2. 1
3. 3

Q. Sophia is enjoying a glass of milk with cookies. if she ate 4 cookies having 40 calories each, then the total calorie intake from the cookies is

1. 160

Q. The cost of pizza varies directly as the square of its radius. If a pizza with radius 6 inches costs 9 $\$$, then the cost of a 12 inch pizza is

1. $\$30$
2. $\$27$
3. $\$36$