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3-D Mensuration || 10.02.2021

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Question 1

Two spheres of equal radius are taken out by cutting from a solid cube of side cm. What is the maximum volume (in cm3) of each sphere?

Question 2

Three toys are in the shape of the cylinder, hemisphere, and cone. The three toys have the same base. The height of each toy is 2√2 cm. What is the ratio of the total surface areas of the cylinder, hemisphere and cone respectively?

Question 3

A cube is cut into 8 parts using 3 cuts. Find the net increase in its total surface area.

Question 4

A square is inscribed in a quarter circle in such a way that two of its adjacent vertices on the radius are equidistant from the centre and other two vertices lie on the circumference. If the side of square is , then what is the radius (in cm) of the circle?

Question 5

A square has its side equal to the radius of sphere. The square revolves round a side to generate a surface of total area S. If A be the surface area of the sphere, which one of the following is correct?

Question 6

Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The radius of the new sphere (in cm) is:

Question 7

A cuboid of size 60cm × 40cm × 36cm is cut into 8 identical part by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?

Question 8

The base of a prism is a trapezium. The lengths of the parallel sides of the trapezium are 15 cm and 18 cm respectively and the distance between the parallel sides is 10 cm. If the volume of the prism is 1485 cm3, then the height of the prism is:

Question 9

Respective ratio of volume of two cones is 8 : 9 and respective ratio of their heights is 2 : 3 then what is ratio of their radius?

Question 10

The radius of two cylinders are in the ratio of 3:2 and their heights are in the ratio 3:7. The ratio of their volumes is :
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