Sphere — CAT Previous-Year Questions
6 previous-year questions on Sphere from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Sphere · CAT PYQs
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq. cm., and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is:
Each question is followed by two statements A and B. Answer each question using the following instructions.
Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.
Mark (4) if the question cannot be answered on the basis of the two statements.
ABC Corporation is required to maintain at least 400 Kilolitres of water at all times in its factory, in order to meet safety and regulatory requirements. ABC is considering the suitability of a spherical tank with uniform wall thickness for the purpose. The outer diameter of the tank is 10 meters. Is the tank capacity adequate to meet ABC’s requirements?
A. The inner diameter of the tank is at least 8 meters.
B. The tank weighs 30,000 kg when empty, and is made of a material with density of 3 gm/cc.
Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be
There are 8436 steel balls, each with a radius of 1 centimetre, stacked in a pile, with 1 ball on top, 3 balls in the second layer, 6 in the third layer, 10 in the fourth, and so on. The number of horizontal layers in the pile is
The diameter of a hollow cone is equal to the diameter of a spherical ball. If the ball is placed at the base of the cone, what portion of the ball will be outside the cone?