Hemisphere: Surface Area & Volume MCQs Quiz | Class 9

This Class IX Mathematics (Code 041) quiz focuses on Unit V: Mensuration, specifically the topic of Hemispheres. The questions cover curved surface area, total surface area, and volume calculations. Test your understanding of these concepts, check your score immediately, and download the solution PDF for revision.

Overview of Hemisphere Formulas

A hemisphere is obtained by cutting a sphere into two equal halves. In Class 9 Mensuration, understanding the surface area and volume of a hemisphere is crucial. Unlike a sphere, a solid hemisphere has two surfaces: a curved surface and a flat circular base.

Key Formulas

  • Curved Surface Area (CSA): The area of the outer curved part only. Formula: 2 * pi * r^2.
  • Total Surface Area (TSA): The sum of the curved surface area and the area of the flat circular base (pi * r^2). Formula: 3 * pi * r^2.
  • Volume: The amount of space occupied by the hemisphere. It is exactly half the volume of a sphere. Formula: (2/3) * pi * r^3.

Common Mistakes to Avoid

Students often confuse the Total Surface Area of a solid hemisphere with that of a hollow hemisphere or sphere. Remember that for a solid hemisphere, you must include the base area (pi * r^2) in the calculation. Also, ensure units are consistent (e.g., all in cm or m) before calculating.

Quick Revision List

  • Radius (r): The distance from the center to any point on the surface.
  • Diameter (d): 2 * radius.
  • Pi: Generally taken as 22/7 or 3.14.
  • Units: Area is in square units; Volume is in cubic units.

Extra Practice Questions

  1. Find the volume of a hemisphere with radius 3 cm.
  2. Calculate the curved surface area if the diameter is 20 cm.
  3. If the total surface area is 462 cm^2, find the radius.
  4. Find the ratio of the volume of a sphere to the volume of a hemisphere with the same radius.
  5. A hemispherical bowl has a radius of 3.5 cm. How much water can it hold?