Height & Depth

The concepts of height and depth are routinely used in a wide range of routine daily tasks. One might regularly deal with the concepts of height and depth in one way or another. For instance, we use the concept of height for defining how tall a tower is? How tall is a boy in the class? How high is the building?

Similarly, the concept of depth to define how deep a well is? How deep is the pothole? How deep is the sea?

Simply understood, height could be defined as the vertical distance from base to the highest point of the object. Height is always measured on the vertical axis, and it can be measured in different terms such as cm (centimetres), meters, inches, feet, etc. In similar aspects, depth could be understood as the distance from the topmost point to the bottom of a particular object. Note that the object could be any entity such as a human being, a building, a swimming pool, etc.

**Figure 1 – Rectangular Block**

The above-given figure illustrates a rectangular block in which three different dimensions, i.e. length, width, and height, have been given. To measure the height of this block, we have to consider the lowest point, i.e. the base and highest point, i.e. the top. By calculating the difference between, topmost point and base of block could be defined as height. Thus, the concept of height is fairly simple as we have to only calculate the difference between the topmost point and the bottom-most point. For instance, we would say that the building is 10 m high or 50 m high for denoting its height.

A similar concept could be applied for measuring the depth of an entity, i.e. to calculate the distance between the topmost point and bottom-most point. For instance, if we say that a well is 10 feet deep, then we are telling the difference between topmost point and the bottom point of the well.

Above all, standard units for denoting height or depth are most commonly inches, feet, and meters.

QUIZ

With the help of above-given rudimentary information regarding the concept of heights and depths, try to answer the below-given questions by thinking analytically and logically.

**Q1.**Andrew uses similar size clips for measuring the height of the toy. He founds out that the toy is 3 clips tall. If each clip is 3 inches in length, find out the total height of the toy.

- 10 inches
- 6 inches
- 9 inches
- 12 inches

**Answer – **(c)

**Solution – **Andrew uses three clips to measure the height of the toy figure where each clip has a length of 3 inches. Thus, a total of 3 clips would represent a length of 9 inches in total. Hence, the toy figure has a height of 9 inches.

**Q2. **An under-construction building comprises of 10 floors. The ceiling for each floor is 10 meters high. Find the total height of building in feet.

- 320 feet
- 220 feet
- 300 feet
- 328 feet

**Answer – **(d)

**Solution –** There are a total of ten floors in the building, and the height of the ceiling is 10 m that represents the height of each floor. By multiplying both terms, i.e.,

Number of Floors x Total Height of Each Floor = Height of Building

10 x 10 = 100 meter = Height of Building

As 1 meter = 3.28 feet, 100 meters will be equal to 328 feet. Hence, the correct answer is (d).

**Q3. **A submarine submerges into the ocean from sea level. If it consistently submerges for 25 meters per minute. Find out the depth at which that submarine would be after 4.5 minutes.

- 5 meters
- 5meters
- 5meters
- 5meters

**Answer –**(a)

**Solution – **As the submarine initiated from sea level with a constant speed of 25 meters per minute. Simply understood, every minute the submarine would submerge 25 meters in the sea. Hence, using simple multiplication, we can obtain that after 4.5 minutes, the submarine would submerge to a depth of 112.5 meters.

**Q4. **You have a rectangular tank that is 200 feet long and 20 feet wide which is capable of holding a volume of 30,000 cubic feet of water. Find out the depth of the tank.

- 10 feet
- 5 feet
- 9 feet
- 5 feet

**Answer –**(d)

**Solution – **This problem could be solved with the help of the concept of volume. As the tank is rectangular, we can use the formula

Volume of rectangle = *length* x *width* x *depth*

In this case, we have been given with length, width, and volume, and we are asked to find out the depth of the tank. Here, volume of tank = 30,000 cubic feet, length = 200 feet, and width = 20 feet. Thus, depth could be calculated by

Depth = Volume / (Length x Width)

Depth = 30000/ (200 x 20)

Depth = 7.5 feet.

Hence, the depth of the tank is 7.5 feet. ∴option (d)

**Q5. **Building A has 15 floorswhere each of which has a difference of 15 meters between ceiling and ground. Adjacent to building A, a well is being dug with a speed of 8 meters per day. The well is at a current depth of 40 meters. Find out the difference between the highest point of Building A and the lowest point of the well after two days.

- 150 meters
- 200 meters
- 281 meters
- 56 meters

**Answer – **(c)

**Solution – **In this problem, we need to calculate the height and depth of two different entities and then find out the difference. Firstly,we need to find out the height of the building,

Total Height of Building = Number of Floors x Total Height of Each Floor

Total Height of Building = 15 x 15 m = 225 m.

Further, currently, the depth of well is 40 m, and it is being dug at a speed of 8 meters per day. After two days, 16 m of the well will be dug. Thus, the total depth of the well will increase by 16 m. Hence, total depth would be 40 m + 16 m = 56m.

∴The difference between the topmost point of the building and bottom-most points of well will be equal to 225 m + 56 m = 281 m. Hence, option (c)

**Q6. **Which of the following is true about the concept of height?

- Height can only be measured on the horizontal axis.
- Height can be measured on both vertical and horizontal axis as per preference.
- Height can only be measured on a vertical axis.
- None of the above.

**Answer – **(c)

**Solution – **As per the basic definition of height, it needs to be measured from the base to the top. Thus, the height can only be measured on a vertical axis. Hence, the option (c) is correct.

**Q7. **Heights of Building A, B, C, and D are 65 meters, 125 feet, 3937 inches, and 50 meters. Find out the tallest building amongst four.

- Building A
- Building B
- Building C
- Building D

**Answer – **(c)

**Solution – **We cannot compare the heights ofthe building unless they are given in similar units. For instance, the heights of buildings are given in meters, feet, and inches. Firstly, we will convertthe height of each building in meters.

Building A | Building B | Building C | Building D |

65 m | 1 Foot = 0.3 m 125 Feet = | 1 Inch = 0.02 m 3937 inches = | 50 m |

Thus, comparing all the values, we can conclude that Building C is the tallest amongst all buildings.

**Q8. **Height of Burj Khalifa, the tallest building the world, is 830 m to the tip. If a stunt man base jumps from the tip and descends at a rate of 10 meters per second. How much time would it take him to reach the base of the building?

- 1 Minute 23 Seconds
- 84 Seconds
- 1 Minute 30 Seconds
- 2 Minutes

**Answer – **(a)

**Solution – **As per the given question, the height of building = 830 meters and the rate of descending = 10 meters per second.

Total time to reach the base = height of building / rate of descending

= 830 m / 10 m per second

= 83 seconds = 1 minute and 23 seconds.

Thus, the stunt man will be able to reach the base within 1 minute and 23 seconds.

**Q9. **The current height of a glacier is 2500 meters. Every year the height of glacier decrements by 0.5 meter primarily due to global warming. Find the height of glacier after 10 years.

- 2505 m
- 2495 m
- 2400 m
- 2480 m

**Answer –**(b)

**Solution – **The current height of the glacier is 2500 meters.

As the height decrements by 0.5 meter per year. In ten years, the height will be reduced by 0.5 x 10 = 5 meters.

Thus, the total height of glacier after ten years would be 2500 m – 5 m = 2495 m.

**Q.10 **Which of the following is not a standard unit to represent height or depth?

- Kilometres
- Centimetres
- Inches
- Pounds

**Answer – **(d)

**Solution – **For representing height or depth, we can use multiple units of distance such as kilometres, centimetres, millimetres, inches, etc. This makes option (a), (b), and (c) correct for denoting height or depth. However, Pound is most commonly used to represent weight. Hence, option (d) could be regarded as incorrect as it can not be used for denoting height or depth under any circumstances.