Jodi says that if you double the radius of a right circular cone and divide the slant height by 2, then the surface area of the cone stays the same since the 2s cancel each other out. How do you respond?

a. Which will increase the volume of a right circular cylinder more: doubling its height or doubling its radius? Explain.
b. Is your answer the same for a right circular cone? Why?

Flame cells (a) collect excess water (b) respond to light $(c)$ produce eggs (d) produce sperm .

Lewis and Clark's __ inspired many Americans to move west .

Andrica's conjecture, named after Dorin Adrica, claims that $A_{n}=\sqrt{p_{n+1}}-\sqrt{p_{n}}<1$ for all positive integers n, where $p_n$ denotes the nth prime. Gather evidence for this conjecture by computing $A_n$ for as many positive integers n as you can. From your work, make a conjecture about the largest value of $A_n$.

Heron’s formula can be used to find the area of a triangle if the lengths of the three sides are known. If the lengths of the three sides are a, b, and c units and the semiperimeter s =$\frac {a + b + c} 2$ , then the area of the triangle is given by $\sqrt {s(s - a)(s - b)(s - c)}$. Use Heron’s formula to find the areas of the right triangles with the sides given.
a. 3 cm, 4 cm, 5 cm
b. 5 cm, 12 cm, 13 cm

The napkin ring pictured is to be resilvered. How many square centimeters of surface area must be covered?

a. Find many different types of cans that are in the shape of a cylinder. Measure the height and diameter of each can.
b. Compute the surface area and volume for each can.
c. Based on the information collected, make a recommendation for designing an “ideal” can.

Find the surface area of a right square pyramid if the area of the base is 169 $cm^2$ and the slant height of the pyramid is 13 cm.

A student asks why $\frac {22} 7$ cannot always be used as the value of $\pi$. How do you respond?

Find the surface area of a right square pyramid if the area of the base is 100 $cm^2$ and the height of the pyramid is 20 cm.

List the following in decreasing order: 8 m, 5218 cm, 245 cm, 91 m, 6 m, 925 mm.

An Olympic-sized pool in the shape of a right rectangular prism is 50 m $\times$ 25 m. If it is 2 m deep throughout, how many liters of water does it hold?

List the following in decreasing order: 8 cm, 5218 mm, 245 cm, 91 mm, 6 m, 700 mm.