Largest sphere inside a cube or box: empty space or sphere surface area
This type of question, asked 5 times: 18 Sep 2025 S2, 19 Sep 2025 S1, 23 Sep 2025 S1, 23 Sep 2025 S3, 24 Sep 2025 S1. All 5 questions below, oldest first.
Try each one first, then open its answer.
Question 1
18 Sep 2025 S2
60A marble is spherical in shape with a radius of 4 cm. If the marble is placed inside a cube with side length 10 cm, what is the volume of the cube that is not occupied by the marble?Tap an option to check your answer.
Question 2
19 Sep 2025 S1
61A solid sphere is placed inside a cube such that it touches all six faces. What percentage of the cube's volume is not occupied by the sphere?Tap an option to check your answer.
Question 3
23 Sep 2025 S1
54A sphere is inscribed inside a cube. The volume of the cube is 1728 . What is the total surface area of the sphere?Tap an option to check your answer.
Question 4
23 Sep 2025 S3
55A perfect cube with a side length of 8 cm has the largest possible sphere fitted inside it. What is the volume of the empty space within the cube?Tap an option to check your answer.
Question 5
24 Sep 2025 S1
55A rectangular tank measures 12 cm long, 10 cm wide, and 6 cm high. If a spherical ball of the largest possible size is placed inside this tank, what is the volume of the space not occupied by the ball?Tap an option to check your answer.