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Cube and Cuboid Problems: Geometry Exercises, Cheat Sheet of Mathematics

PGDAV CollegeMathematics

A series of exercises focused on the properties and calculations related to cubes and cuboids. It covers various aspects of these geometric shapes, including volume, surface area, and diagonal length. The exercises are designed to test understanding of fundamental geometric concepts and problem-solving skills in three-dimensional space.

Typology: Cheat Sheet

2022/2023

Uploaded on 12/13/2024

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Cube and cuboid sheet 3
1. The length and breath of a room are 21 cm and 16 m
respectively . If the length of the longest rod that can
be placed in the room is 29 m , then what is the
height of the room ?
a. 10 m
b. 12 m
c. 11 m
d. 13 m
2. The lenght of a room is 21/16 times its breadth and
breadth is 4/3 times its height . If H is the height of
the room and L is the longest rod that can be placed
in the room, then which one of the following is
correct ?
a. 12L = 29H
b. 9L = 25H
c. 7L = 23H
d. 5L = 13H
3. Let X, Y, Z be the length , breadth, height of a cuboid.
If its volume is 400 cubic cm and total surface area is
340 square cm, then what is X–¹ + Y–¹ + Z–¹ equal
to ?
pf3
pf4
pf5

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Cube and cuboid sheet 3

  1. The length and breath of a room are 21 cm and 16 m respectively. If the length of the longest rod that can be placed in the room is 29 m , then what is the height of the room? a. 10 m b. 12 m c. 11 m d. 13 m
  2. The lenght of a room is 21/16 times its breadth and breadth is 4/3 times its height. If H is the height of the room and L is the longest rod that can be placed in the room, then which one of the following is correct? a. 12L = 29H b. 9L = 25H c. 7L = 23H d. 5L = 13H
  3. Let X, Y, Z be the length , breadth, height of a cuboid. If its volume is 400 cubic cm and total surface area is 340 square cm, then what is X–¹ + Y–¹ + Z–¹ equal to?

a. 17/ b. 17/ c. 7/ d. 9/

  1. If the areas of 3 adjiacent faces of a cuboid are X, Y, Z respectively , then the volume of the cuboid is a. X+Y+Z b. √(XYZ) c. 3XYZ d. √( X³+Y³+Z³)
  2. The areas of three adjacent faces of a cuboidal tank are 3m², 12m² and 16m². The capacity of the tank, in litres, is ; a. 48000 b. 24000 c. 72000 d. 36000
  3. The volume of a cuboid is 3600 cubic cm. The areas of two adjacent faces are 225 square cm and 144 cm square cm. What is the area of the other adjacent face? a. 400 square cm b. 360 square cm c. 320 square cm d. 300 square cm
  1. The length breadth and height of a rectangular box are in the ratio 3 : 2 :4 , respectively , and the cost of covering it with a sheet of paper at the rate of 1.50 rupee per square metre is 1950 rupee. Find 50% of the box ( in m³). a. 1600 b. 1750 c. 1800 d. 1500
  2. The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 200% , 300% and 300% respectively. Then compared to the original volume, the increase in the volume of the cuboid will be? a. 47 times b. 26 times c. 17 times d. 15 times
  3. The length ,width and height of a room are in the ratio 5 : 4 : 2. If in a new room, the length is increased by 40% and the width by 25%, how will the

volume of the room change for the total area of the four walls of the room to stay the same as before? a. Reman the same b. Increase by 31.25% c. Increase by 20.25% d. Increase by 10%

  1. A hall of 10 m length , 5 m width and 6 m height is to be painted ( one side only). Determine the total surface area to be painted. a. 300 m² b. 280 m² c. 330 m² d. 230 m²
  2. The length , breadth and height of a hall are 10 m, 20m, and 15m, respectively. Find the cost of whitewashing the walls of the inside of the hall and ceiling at the rate of 10.20 rupee/ m² a. 13, b. 11, c. 15, d. 16,
  3. A hall is 18 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to
  1. The length of a diagonal of a cuboid is 11 cm. The surface area is 240 square cm. What is the sum of its length,, breadth and height? a. 16 cm b. 17 cm c. 18 cm d. 19 cm
  2. The sum of the length, breadth and height of a cuboid is 23 cm, and its diagonal is 5√7 cm. Its surface area is : a. 144 cm² b. 177 cm² c. 188 cm² d. 111 cm²
  3. The sum of the length , breadth and height of a cuboid box is 20 cm and the total surface area of cuboid is 256 sq. Cm. What is the maximum length of a stick that can be placed inside the cuboid box? a. 16 cm b. 24 cm c. 32 cm d. 12 cm