Word Problems on SA/Volume MCQs Quiz | Class 9

This interactive quiz for Class IX Mathematics (Code 041) focuses on Unit V: Mensuration, specifically covering mixed word problems on the Surface Area and Volume of spheres, hemispheres, and cones. Test your problem-solving skills, view your score immediately, and download the detailed answer key as a PDF.

Overview of Mensuration (Sphere, Hemisphere, Cone)

In Class 9 Mathematics, Unit V (Mensuration) introduces solids involving curved surfaces. Solving word problems requires visualizing the shape, identifying the correct dimensions (radius, height, slant height), and applying the appropriate surface area or volume formula.

Key Formulas

Shape Surface Area Volume
Sphere 4 * pi * r * r (4/3) * pi * r * r * r
Hemisphere CSA: 2 * pi * r * r
TSA: 3 * pi * r * r		 (2/3) * pi * r * r * r
Cone CSA: pi * r * l
TSA: pi * r * (l + r)		 (1/3) * pi * r * r * h

Note: ‘l’ is slant height, ‘r’ is radius, ‘h’ is vertical height. For a cone, l = sqrt(h*h + r*r).

Problem Solving Tips

  • Melting and Recasting: When a solid is melted to form another, the volume remains constant. (Volume of Solid A = Volume of Solid B).
  • Capacity: Capacity usually refers to the internal volume of a hollow object.
  • Units: Ensure all dimensions are in the same unit (cm vs m) before calculation. Surface area is in square units; volume is in cubic units.

Extra Practice Questions

  1. Find the volume of a sphere whose surface area is 154 sq cm.
  2. A conical tent is 10 m high and the radius of its base is 24 m. Find the slant height of the tent.
  3. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
  4. Find the total surface area of a cone if its slant height is 21 m and diameter of its base is 24 m.
  5. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.