CAT 2024 Geometry & Mensuration Question (Hard)

Question

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

Accepted Answer

Step 1 Let the sides of the box be , , and . We are given Also, Step 2 Since the box is inscribed in a sphere, the space diagonal of the box is equal to the diameter of the sphere. Let be the diagonal To find , use identity Substitute values So, the diagonal Step 3 Volume of the sphere is , so Thus,

CAT 2024

Quantitative

Geometry & Mensuration

Hard

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

From CAT Score to IIM Selection!

Practice

Features

Support