Math Problem Statement

Given various mathematical problems involving surface area, volume, and real-world applications of prisms, cylinders, and rectangular structures, as shown in the provided image.

Solution

Let’s break this down question by question with explanations where required. If you'd like me to solve any specific question, let me know!

Here is a summary of the questions in the image:


  1. Question 3

    • A trapezoidal prism is to be electroplated at a rate of Rs 25 per square meter.
    • Find the expenditure for electroplating.
    • Also, calculate the volume of the prism.
  2. Question 4

    • Frame real-life problems based on surface area: i) Surface area of face A and its opposite face.
      ii) Surface area of faces B & C and their opposites.
      iii) Total surface area.
  3. Question 5

    • A rectangular prism aquarium with:
      • Base = 180 cm × 70 cm
      • Height = 121 cm
    • Find the glass area used when:
      • The top is open.
      • 0.5% glass is wasted.
  4. Question 6

    • Tobacco companies label 85% of the surface area of cigarette packs with warnings.
    • You need to:
      • Label the area with dimensions and add a picture.
  5. Question 7

    • A hexagonal prism pen stand has:
      • Side of hexagon = 3 cm
      • Height = 9 cm
    • The stand is open at one end.
    • Find its total outer surface area.
  6. Question 8

    • Calculate the total surface area and volume of the given prism in the diagram.
  7. Question 9

    • Find the total surface area of a cylinder with:
      • Radius = 7 cm
      • Height = 15 cm.
  8. Question 10

    • A cylinder-shaped can has:
      • Height = 12 cm
      • Radius = 3.5 cm
      • Label has an overlap of 1.5 cm vertically.
    • Find the area of the paper label.

Would you like me to solve a particular question? For example:

  • Calculating the volume or surface area in specific problems?
  • Converting to step-by-step solutions?

5 Related Questions

  1. How do you calculate the surface area of a trapezoidal prism?
  2. What is the process for finding the total surface area of a hexagonal prism?
  3. How do you calculate glass waste in percentage for rectangular aquariums?
  4. What formula is used to calculate the curved surface area of a cylinder?
  5. How do you account for overlaps in surface area calculations?

Tip: To calculate the total surface area, always include both lateral (curved) and base areas in your formula. Let me know if you need specific explanations!

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Math Problem Analysis

Mathematical Concepts

Surface Area
Volume
Prisms
Cylinders
Percentage Wastage
Real-World Applications of Geometry

Formulas

Surface Area of a Prism = Lateral Area + Base Areas
Volume of a Prism = Base Area × Height
Surface Area of a Cylinder = 2πr(h + r)
Volume of a Cylinder = πr²h
Percentage Wastage = (Wastage / Total Area) × 100

Theorems

Basic principles of geometry for prisms and cylinders
Area and volume relationships in 3D shapes

Suitable Grade Level

Grades 8-10