Question

determine (a) the volume and (b) the surface area of the three-dimensional figure. use the \\(\pi\\) key on your calculator.

a) the volume is
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

b) the surface area is
(simplify your answer. type an integer or a decimal rounded to the nearest hundredth as needed.)

Explanation:

Identify given dimensions

We are given a cone with:

• Diameter \(d = 5\text{ ft}\), which means the radius is:

$$r = \frac{d}{2} = 2.5\text{ ft}$$

• Height \(h = 23\text{ ft}\).

Calculate the volume

Using the Volume of Cone knowledge point

$$
LATEXBLOCK0
$$

Find the slant height

Using the Pythagorean Theorem knowledge point

$$
LATEXBLOCK1
$$

Calculate the surface area

Using the Surface Area of Cone knowledge point

$$
LATEXBLOCK2
$$

Round to the nearest hundredth

Rounding the calculated values:

• Volume: \(150.53\text{ ft}^3\)
• Surface area: \(201.34\text{ ft}^2\)

Answer:

Question 1

a) The volume is <blank>150.53</blank> <blank>\(\text{ft}^3\)</blank>

Question 2

b) The surface area is <blank>201.34</blank> <blank>\(\text{ft}^2\)</blank>