Answer: 2.1 km
Step-by-step explanation:
Given
A road map has a scale of 
The length of road on the map is 
The ratio of length on the map to the length on road is 1:30,000
Suppose x is the length of real road

Answer:

Step-by-step explanation:
-Given that the dimensions of the new deck are double the dimensions of the old deck:

#The area of the new deck can now be calculated as:

Hence, the area of the new deck is 
Answer:
a. 5.25cm
b. 374.6 cm^2
Step-by-step explanation:
The radius of the conical cup is half the length of the arc formed
Mathematically, the length of the arc would be;
L = theta/360 * 2 * pi * r
L = 135/360 * 2 * 22/7 * 14 = 33 cm
Now, the arc of this sector will become the base circumference of the circular base of the cone
Thus;
2 * pi * R = 33
2 * 22/7 * R = 33
R = (7 * 33)/44 = 5.25 cm
b. The volume of the cone
Kindly note that the radius of the circle becomes the height of the cone
Mathematically;
V = 1/3 * pi * r^2 * h
Kindly note that the radius of the circle will become the slang height of the cone
We can use pythagoras’ theorem to find the height of the cone
Pythagoras theorem states that the square of the hypotenuse equals the sum of the squares of the two other sides
So here, slant height l is the hypotenuse, h and r are the other two sides
So 14^2 -5.25^2 = h^2
h^2 = 168.4375
h = 12.98 cm
Volume is thus ;
1/3 * pi * 5.25^2 * 12.98 = 374.6 cm^3
Answer:
<em>The tank's capacity is 500 liters</em>
Step-by-step explanation:
<u>Proportions</u>
The tank initially contains 50 liters of water. The tank's capacity is more than that, as we'll show later.
We know after 20 minutes of leaking from the tank, 40 liters still remain. This means 10 liters have leaked in 20 minutes. The loss of water occurs at a constant rate or 10/20=0.5 liters per minute.
After 30 more minutes, the tank has lost 0.5*30 = 15 more liters of water and now has 40 - 15 = 25 liters remaining.
We are told those 25 liters correspond to 5% of the tank's full capacity. Thus, the full capacity of the tank is:

The tank's capacity is 500 liters