# Use the image to answer the question.

A cone is marked with a height of 12 centimeters and a diameter of 11 centimeters, both shown as perpendicular dotted lines. The slant height is 9 centimeters.

What is the height of the right circular cone?

5.5 cm

12 cm

9 cm

11 cm

## The correct answer is 9 cm.

## Bot.

Use the image to answer the question.

An oblique cylinder is labeled with a height of 15 centimeters and radius 5 centimeters.

Find the surface area of the cylinder below. Use the approximation 3.14 for pi.

A. 628 square centimeters

B. 533.8 square centimeters

C. 628 centimeters

D. 1,099 square centimeters

## To find the surface area of a cylinder, we use the formula 2πrh + 2πr^2.

Given:

Height (h) = 15 cm

Radius (r) = 5 cm

Approximation of pi (π) = 3.14

Calculating the surface area:

Surface Area = 2πrh + 2πr^2

= 2(3.14)(5)(15) + 2(3.14)(5^2)

= 471 + 157

= 628 square centimeters

Therefore, the surface area of the cylinder is 628 square centimeters. The correct answer is A. 628 square centimeters.

## Bot.

Adrian is painting the outside of a cylinder tire he plans to recycle as a planter. The tire has a radius of 4 feet and a height of 3 feet. In order to understand how much paint is needed, Adrian wants to know the surface area of the outside of the tire. How many square feet is the outside of the tire? Use 3.14 for pi and round your answer to the nearest tenth.

## To find the surface area of the outside of the tire, we need to calculate the lateral surface area of the cylinder, which excludes the top and bottom circles.

Given:

Radius (r) = 4 feet

Height (h) = 3 feet

The formula for the lateral surface area of a cylinder is 2πrh, where r is the radius and h is the height.

Calculating the surface area:

Surface Area = 2πrh

= 2(3.14)(4)(3)

= 75.36 square feet (rounded to the nearest tenth)

Therefore, the outside of the tire has a surface area of approximately 75.4 square feet.

## Eli is making a model castle out of clay. One of the roof peaks is in the shape of a cone with a diameter of 14 inches and a slant height of 20 inches. What is the surface area of the cone peak? Round your answer to the nearest hundredth. Use 3.14 for pi.

## To find the surface area of the cone peak, we need to calculate the curved surface area, which includes only the curved surface of the cone.

Given:

Diameter (d) = 14 inches (radius = 7 inches)

Slant height (l) = 20 inches

To find the height (h) of the cone, we can use the Pythagorean theorem:

h = √(l^2 - r^2)

h = √(20^2 - 7^2)

h ≈ √(400 - 49)

h ≈ √351

h ≈ 18.73 inches (rounded to the nearest hundredth)

The surface area of a cone is given by the formula πrl, where r is the radius and l is the slant height.

Calculating the surface area:

Surface Area = πrl

= (3.14)(7)(20)

≈ 439.82 square inches (rounded to the nearest hundredth)

Therefore, the surface area of the cone peak is approximately 439.82 square inches.

## Bot.

Use the image to answer the question.

A 3D cylinder shows a base radius of 8 millimeters and perpendicular height of 13 millimeters. A right angle is formed at the center of the base.

Find the volume of the cylinder, in cubic millimeters. Round your answer to the nearest hundredth.

## To find the volume of a cylinder, we use the formula V = πr^2h, where r is the radius and h is the height.

Given:

Radius (r) = 8 millimeters

Height (h) = 13 millimeters

Using the value of pi as 3.14, we can calculate the volume of the cylinder:

Volume = πr^2h

Volume = (3.14)(8^2)(13)

Volume = (3.14)(64)(13)

Volume ≈ 2631.68 cubic millimeters (rounded to the nearest hundredth)

Therefore, the volume of the cylinder is approximately 2631.68 cubic millimeters.

## Bot.

A water bottle has a height of 16 inches and a radius of 4 inches. What is the volume, in cubic inches, of the water bottle? Use 3.14 for pi.