A cistern 8 m long and 6 m wide contains water up to a depth of 2 m. What is the area of the wet surface?

DSSSB -28 August 2019 (Shift-2)

Non Nursing Subjects

Hard

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The wet surface area is the sum of the area of the base and the area of the four vertical walls that are in contact with the water.
Area of the base = Length × Width = 8 m × 6 m = 48 m².
Area of the two longer wet walls = 2 × (Length × Water Depth) = 2 × (8 m × 2 m) = 32 m².
Area of the two shorter wet walls = 2 × (Width × Water Depth) = 2 × (6 m × 2 m) = 24 m².
Total wet surface area is the sum of these areas: 48 m² + 32 m² + 24 m² = 104 m².

Option A: This is an incorrect sum of the component areas. It may result from a calculation error or by incorrectly omitting one of the surfaces, such as one of the pairs of walls.
Option C: This value is significantly smaller than the actual area. It might be the result of calculating only a fraction of the total area, for instance, by omitting the base and some of the walls.
Option D: This value (52 m²) is exactly half of the correct answer (104 m²). This error could occur if one calculates the area of only one long wall and one short wall and adds them to the base (48 + 16 + 12 = 76, incorrect) or forgets to include the base area and makes a calculation error.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the surface area of a cuboid (rectangular prism) partially filled with a liquid as background academic context rather than a clinical decision trigger.
This type of calculation is a fundamental skill applicable in various practical, non-clinical scenarios, such as determining the amount of paint needed to coat the inside of a tank or the quantity of lining material required.
In a public health context, calculating the wet surface area of a water reservoir is crucial for determining the correct amount of disinfectant (like chlorine) needed to treat the water effectively.
Understanding how to calculate surface area is a foundational mathematical skill that is a prerequisite for more complex calculations in science and engineering, including calculating drug dosages based on Body Surface Area (BSA) in healthcare.

How to Approach the Question

First, carefully read the problem to identify the shape of the container (a rectangular cistern) and all the given dimensions (length, width, and water depth).
Next, visualize or sketch the object and identify all the surfaces that are 'wet'. In this case, it's the single bottom surface and the four vertical side surfaces.
Calculate the area of each of these surfaces individually using the formula for the area of a rectangle (Area = length × width).
Remember that the side walls come in pairs (two long walls, two short walls). Calculate the area for one wall in each pair and multiply by two.
Sum the areas of all the individual wet surfaces (the base + the four walls) to find the total wet surface area.
Finally, compare your calculated total with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Calculating the surface area of a cuboid (rectangular prism) partially filled with a liquid.
Stem keywords: cistern, long, wide, depth, area, wet surface
Lead-in keywords: What is
Negative lead-in flag: false

QDxKD0dqcLbHuJ3Nu2ZwhN