Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphere that can be packed inside the cube shaped box? Give you answer rounded to the nearest whole cubic inch

Sagot :

oladayoademosu

Answer:

6283 in³

Step-by-step explanation:

The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.

Since the cardboard box is in the shape of a cube, its volume V = L³

So, L = ∛V

Since V = 12000 in³,

L = ∛(12000 in³)

L= 22.89 in

So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2

So, V = 4π(L/2)³/3

= 4πL³/8 × 3

= πL³/2 × 3

= πL³/6

= πV/6

= π12000/6

= 2000π

= 6283.19 in³

≅ 6283.2 in³

= 6283 in³ to the nearest whole cubic inch

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.