Show:
Volume I
Volume II
Freaky Fractions
Area/Perimeter I
Edges/Vertices/Faces
100
What is the volume of a cone that has a diameter of 16 inches and a height of 4 inches
Answer: 268.08 inches cubed How to get it: First you must find the area of the circular base. In order to do that you need the RADIUS so divide the diameter by 2. SO, you take 8 times 8 times pi to get the area of the base. Take that times the height. Then, since it is a cone, you have to divide that answer by 3.
100
Ethan D bought a kiddie pool so he could swim in it this summer. It was in the shape of a cylinder. It was 2 feet tall and had a radius of 3 feet. What is the volume of Ethan's new kiddie pool?
Answer : Ethan's pool holds about 56.54 feet cubed of water How to get it: Find the area of the circular base by taking 3 times 3 times pi. Then multiply that answer by the height of the cylinder which is 2.
100
What is 5/8 time 2 and 1/4?
Answer: 45/32 or 1 and 13/32 How to get it: First, make 2 and 1/4 into an improper fraction. Then, multiply the numerators and put that answer in the numerator of your answer. Then multiply the denominators and put that answer in the denominator of your answer.
100
What is the area of a triangle with a base length of 8.5 inches and a height of 6.5 inches?
Answer: 27.625 square inches How to get it: Multiply the base length of 8.5 times the height of 6.5 and then divide that by 2.
100
If a polyhedron has 6 faces and 12 vertices, how many edges does it have?
Answer: 16 edges How to get it: Add the faces to the vertices and then subtract two. (That is the formula for finding the number of edges a polyhedron has)
200
What is the volume of a rectangular pyramid with a height of 7 feet and a rectangular base that measures 4 feet by 6 feet.
Answer: 56 feet cubed How to get it: Find the area of the base by taking 4 feet times 6 feet. Then we multiply that answer by the height of 7 feet. Finally, since it is a pyramid, we have to divide that answer by 3.
200
Riley has a diamond in the shape of a hexagonal pyramid. The hexagonal base has an area of 144 square inches. The pyramid is 9 inches tall (it's a big diamond). What is the volume of Riley's diamond?
Answer: 432 cubic inches How to get it: Take 144 (area of the base) times 9 (the height of the pyramid) and then divide by 3 (because it is a PYRAMID)
200
Dean made a batch of 24 cookies. He gave 1/3 of them to Caleb. How many cookies does Dean have left?
Answer: Dean has 16 cookies left. How to get it: Find 1/3 of 24 by dividing 24 by 3 and then taking that times 1. That gives you 8. 8 cookies are how many Dean gave to Caleb so you have to take 8 away from 24 to find how many cookies Dean has left.
200
What is the area of a circle with a diameter of 12? What is the circumference of the same circle?
Answer: Area = 113.09 square inches / Circumference = 37.69 inches How to get it: Area you take the radius times the radius times pi. For the Circumference you take the diameter times pi.
200
There are two geometric solids that are polyhedron. What are they?
Answer: Prism and Pyramid How to get it: YOU SHOULD JUST KNOW THIS, AND YOU MUST HAVE BOTH ANSWERS TO EARN THE POINTS!!!!!!!!!!!
300
What is the volume of a triangular prism if it has the following measurements: Triangular base - base length of 6cm and height of 8cm Height of the Prism - 9cm
Answer: 216 centimeters cubed How to get it: Find area of the base by taking 6 cm times 8 cm. Then, since it is a prism, we just take that area of the base times the height of 9 cm.
300
Samantha has a glass of water. The glass is a cylinder with a height of 8 inches. The diameter of the glass 3 inches. If the glass is 1/4 full of lemonade. How many cubic inches of lemonade are in the glass?
Answer: There are about 14.13 cubic inches of lemonade in Samantha's glass. How to get it: Find the area of the base by taking 1.5 times 1.5 times pi. Then multiply that by the height of 8 inches. Finally, divide by 4 because you need 1/4th of the total volume of the glass since the glass is only 1/4th full.
300
What is 3 and 1/2 times 2 and 1/3 ?
Answer: 49/6 or 8 and 1/6 How to get it: First make the mixed numbers into improper fraction. 3 and 1/2 becomes 7/2. 2 and 1/3 becomes 7/3. Multiply 7/2 times 7/3 by multiplying the numerators and then multiplying the denominators.
300
What is the area of a triangle with a base length of 15 cm and a height of 7 cm?
Answer: 52.5 square centimeters How to get it: Take the length of the base (15 cm) times the height (7 cm) and divide by 2.
300
Tell me how many face, vertices, and edges a rectangular pyramid has.
Answer: 5 faces, 5 vertices, and 8 edges. YOU MUST HAVE ALL ANSWERS CORRECT TO GET THE POINTS!!!
400
Alex bought an ice cream cone, and believe it or not the cone was in the perfect shape of a cone. Half of the radius of the base measured 2 inches and the height of the cone was 5 inches. How many cubic inches of ice cream can the cone hold?
Answer: Alex's cone can hold about 83.77 cubic inches of Ice Cream. How to get it: Find the area of the circular base by taking 4 times 4 times pi (because HALF of the radius is 2 inches). Then multiply that by the height of 5 inches. Finally, since it is a cone you have to divide all that by 3.
400
Sarah is going to ship something in a box that is shaped like a triangular prism. The prism is 32 inches tall. The triangular base has a base length of 4 inches and a height of 3 inches. What is the volume of the box that Sarah is going to use?
Answer: Sarah's box has a volume of 192 cubic inches. How to get it: Find the area of the triangular base first. Do that by taking 4 times 3 and then dividing by 2. Then, take that answer times the height of 32 inches.
400
What is 3 and 1/4 times 2 and 2/3 ?
Answer: 104/12 or 52/6 or 26/3 or 8 and 2/3
400
Jack's backyard has a circular patch of grass in it. The circular patch has a diameter of 34 feet. How much square footage is in the circular patch of grass?
Answer: 907 square feet of grass How to get it: Find the radius of the circle (which is 17 feet) and then multiply 17 times 17 times pi.
400
What geometric solids have either a vertex or vertices?
Answer: pyramid, prism, and a cone YOU MUST HAVE ALL OF THEM TO EARN THE POINTS
500
Maddie has a large, hollowed out, dice (it's a cube). One side of it is 8 inches long. Maddie wants to drink soda pop out of the dice. How many cubic inches of soda pop could her dice hold?
Answer: The dice could hold 512 cubic inches of soda pop How to get it: It is a cube so all of the sides are the same length. To find the volume of a cube you find the area of the base and times that by the height. So you just multiply 8 times 8 to get the area of the base. Then multiply that by 8 since 8 is the height.
500
Natalie has a rock that is in the shape of an octahedron (remember that is two pyramids stuck together). The pyramid that makes up half of the octahedron has a height of 4 inches and a square base with a side length of 4 inches. What is the volume of Natalie's octahedron rock?
Answer: Natalie's rock has a volume of about 42.66 cubic inches. How to get it: First, find the volume of the pyramid that makes up half of the octahedron. Do that by taking 4 times 4 times 4 and then divide by 3. Take that answer times 2 since the octahedron is made up of 2 of the pyramids you just found the volume of.
500
Karrie and Alexis both love pizza. Alexis took 1/2 of a pizza and gave 1/5 of the 1/2 to Karrie. What fraction of the whole pizza did Karrie get?
Answer: Karrie got 1/10 of the whole pizza. How to get it: All you have to do is find 1/5 of 1/2. You do that by multiplying the two fractions. Take the numerators times eachother and then the denominators times eachother.
500
What is the circumference of a circle that has a radius of 9 inches?
Answer: 56.54 inches How to get it: First you have to take the radius times 2 to get the diameter. Then you take the diameter (18 inches) times pi.
500
If there is a truncated rectangular pyramid, how many faces, vertices, and edges does it have?
Answer: 6 faces, 8 vertices, 12 edges How to get it: You have to know what truncated means, and then just visualize the solid in your mind. Notice that the faces + vertices - 2 works for this as well!!