Geometry Answers

(1) Describe the key concepts in transformation geometry. Use illustrations/drawings or examples to support your argument in each case.

(2) Think of any situation in your everyday life in which you can experience transformation geometry. Illustrate your answers. 

Suggest a sequence of statements that logically prove that the angles opposite the

congruent sides of an isosceles triangle are equal in size. Explain each statement simply

and clearly. Use illustrations throughout to enhance your explanations.

1. A lampshade is in the form of a frustum of a cone of which the top and the bottom radius is thrice the top radius, and the height is 14cm.

The volume of the lampshade is 763cm³

Find:

a. The area of material required to cover the lampshade

b. Bottom Radius ?

3. The number of goldfish in a tank is 22, and the volume of the tank is 56 cubic feet. What is the density of the tank?

0.34 goldfish per cubic foot

0.39 goldfish per cubic foot

1.41 goldfish per cubic foot

2.55 goldfish per cubic foot

4. The population of Tinyville is 16.2 Tinys per acre. Exactly 405 Tinys live in Tinyville. How many acres is Tinyville? Only enter a numerical value in the answer blank. Numerical Answers Expected

1. A weather balloon holds 2,850 cubic meters of helium. The density of helium is 0.1685 kilograms per cubic meter. How many kilograms of helium does the balloon contain? Please round your answer to the nearest whole number. Only enter a numerical value in the answer blank. Numerical Answers Expected

2.

The Pretty Pizza Company wants to open a new pizza place either on the north side of town or the south side of town. They want to open the pizza place where the ratio of pizza places per person is less than 0.01. The population of 15 blocks of the north side of town is 221 people per block, but there are already 32 pizza places in the area. The population of 22 blocks of the south area is 150 people per block, and there are 28 pizza places in the area. Where, if anywhere, should the Pretty Pizza Company open a new pizza place?

South side of town

North side of town

Both sides of town

Neither side of town

A grain silo is shown below:

Grain silo formed by cylinder with radius 6 feet and height 168 feet and a half sphere on the top

What is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi.

19,008 ft3

19,461 ft3

6,336 ft3

453 ft3

A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom, as shown below:

Snow cone with spherical bubble gum ball at the bottom

The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?

11.15 in3

11.22 in3

0.07 in3

33.67 in3

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:

Each cone of the hourglass has a height of 12 millimeters. The total height of the sand within the top portion of the hourglass is 47 millimeters. The radius of both the cylinder and cone is 4 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?

6.4

62.4

8.5

56.0

Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B is a square pyramid with a base side length of 36 inches and a height of 24 inches. How many times bigger is the volume of pyramid B than pyramid A?