Areas of plane figures and surface areas/volumes of cubes, cuboids, cylinders, cones and spheres.
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Q1 · Mensuration · EASY
A cylinder and a cone have equal radii of 7 cm and equal heights of 12 cm. What is the ratio of the volume of the cylinder to the volume of the cone?
Q2 · Mensuration · MEDIUM
A rectangular park 45 m long and 30 m wide has two paths of equal width running parallel to its length and breadth through the center. If the area of the paths is 234 m², what is the width of each path?
Q3 · Mensuration · HARD
A hemispherical bowl of radius 9 cm is filled completely with water. This water is then poured into a conical flask of radius 9 cm. If the water fills the flask to the brim, what is the height of the conical flask?
Q4 · Mensuration · MEDIUM
A cubical block of side 10 cm is surmounted by a hemisphere of maximum possible diameter. What is the total surface area of the solid thus formed? (Take π = 22/7)