True or False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counter example.

$\left(a\right)$True or False: If a square grows larger, so that its side length increases at a constant rate, then its area will also increase at a constant rate.

$\left(b\right)$True or False: If a square grows larger, so that its side length increases at a constant rate, then its perimeter will also increase at a constant rate.

$\left(c\right)$True or False: If a circle grows larger, so that its radius increases at a constant rate, then its circumference will also increase at a constant rate.

$\left(d\right)$True or False: If a sphere grows larger, so that its radius increases at a constant rate, then its volume will also increase at a constant rate.

$\left(e\right)$True or False: The volume of a right circular cone is one-third of the volume of the right circular cylinder with the same radius and height.

$\left(f\right)$True or False: If $V\left(r\right)$is the volume of a sphere as a function of its radius, and $S\left(r\right)$is the surface area of a sphere as a function of its radius, then $V^{\text{'}}\left(r\right)=S\left(r\right)$.

$\left(g\right)$True or False: If you unroll the side of a right circular cylinder with radius $r$and height $h$, you get a flat rectangle with height $h$and width $2\pi r$.

$\left(h\right)$True or False: Given a right triangle with side lengths $a$and $c$and hypotenuse of length $b$, we must have $a^2+b^2=c^2$.

Step by step solution

01

v

v

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!