Question 3

A rectangular prism has dimensions 3 inches, 4 inches, and 5 inches. Find the dimensions of another
rectangular prism with the same volume but less surface area.

What are the dimensions of the shape? *

What is its surface area?*

Step-by-step explanation:

The formula for finding the volume is

Volume = length × width × height

Volume of the given prism is

Volume = 3 × 4 × 5 = 60 inches³

The formula for determining the surface area of a rectangular prism is expressed as

Surface area = Ph + 2B

Where

P represents perimeter of base

h represents height of prism

B represents base area

Perimeter of base = 2(length + width)

P = 2(3 + 4) = 14 inches

B = 3 × 4 = 12 inches

h = 5 inches

Surface area = 14 × 5 + 2 × 12 = 94 inches²

For another prism,

Assuming h = 3, length = 10 and width = 2, then

Volume = 3 × 10 × 2 = 60 inches³

P = 2(10 + 2) = 24 inches

B = 10 × 2 = 20 inches

Surface area = (24 × 3) + (2 × 20) = 112 inches²

If we keep changing the values, the surface area will always be greater than 94 inches².

Therefore, there is no rectangular prism with the same volume but less surface area.

The correct answer is the greater the mass, the greater the force. The hockey puck will move a greater distance in crash 1 than in crash 2.

Explanation:

The force with which a body moves depends on the acceleration it has and its mass. Since the bodies are solid, inelastic shocks are produced, in which all the energy is transmitted from one body to another. In case 1, the impacting body has a greater mass, producing a greater force on the hockey puck, causing it to travel a greater distance. In the second case, being massless, there will be a crash where the body that impacts will be still and the hockey puck will move less than in case 1.

Have a nice day!