







Two cones formed from two circular sectors 
20181130 

From APARNA: The central angles of two sector of a circle are 60° and 120° . Using these sectors two cones are made. If the radius of the smaller cone is 5 cm, find the radius and base area of the larger cone. Answered by Penny Nom. 





Paving stones area 
20180808 

From Declan: I am thinking of buying some reclaimed block paving stones. There are 750 pieces in total.
60% are L 140mm x W 140mm x H50mm
40% are L170mm x W140mm x H50mm
How much area will this cover? Answered by Penny Nom. 





A two digit number 
20150821 

From Cameron: Write the 2 digit number that matches the clues.
My number has a tens digit that is 8 more than the ones digit. Zero is not one of my digits.
My number is ________. Answered by Penny Nom. 





Filling three holes with stones 
20140820 

From mark: how many tonnes of hardcore/crushed stone would it take to fill
1 hole 9ft diameter 5ft deep
and 2 holes both 3ft diameter and 5ft deep Answered by Penny Nom. 





Two cones 
20140409 

From c.j: what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help. Answered by Penny Nom. 





Cones, pyramids, cylinders and prisms 
20120913 

From Roy: I read on this page that a pyramid is a special kind of cone, but a cone is not a pyramid. Does this apply to cylinders. Is a prism a special kind of cylinder, but a cylinder is not a prism? Answered by Robert Dawson. 





Two conical tanks 
20110217 

From rustom: Two vertical conical tanks (both inverted) have their vertices connected by a short horizontal pipe.
One tank, initially full of water, has an altitude of 6 ft. and a diameter of base 7 ft.
The other tank, initially empty, has an altitude of 9 ft., and a diameter of base 8 ft.
If the water is allowed to flow through the connecting pipe, find the level to which
the water will ultimately rise in the empty tank (Neglect the water in the pipe.) Answered by Penny Nom. 





How long will you and your friend be able to talk? 
20101123 

From beket: you and your friend leave your home town at the same time your friend travels by train 45 mph directly east while you travel by train 50 mph going directly south you are talking on cell phone but you plan charges extra if the phones are 100 miles apart. How long will you and your friend be able to talk before the charges increase? Answered by Penny Nom. 





The cube of an integer 
20100120 

From Shankar: Can the cube of an integer end with 1985 ones ? Answered by Robert Dawson. 





how many ones are in 1 million 
20090917 

From djuan: how many ones are in 1 million Answered by Harley Weston. 





Units digit 
20080702 

From seemachauhan: How to find unit digit of various numbers and what are unit digits? Answered by Penny Nom. 





The sum of the ones 
20071029 

From Hangsun: When 2 two digit numbers are added what is the greatest possible sum of the ones? Answered by Penny Nom. 





Tens and ones 
20070916 

From julia: My son has come home with a math question "what i know about 10s and 1s" we're totally stumped any information you can provide would be greatly appreciated Answered by Harley Weston. 





Two cones 
20061230 

From Cassie: A cone of radius 6 and height 12 and a different cone of radius 8 and height 12 intersect as shown in the figure below, where the vertex of one matches with the center of the base of the other. Find the volume of the intersection of the two cones (in exact form). Answered by Penny Nom. 





How fast is the water level rising 
20060812 

From Erin: Water runs into a conical tank at the rate of 9ft^{3}/min. The tank stands point down and has a height of 10 ft. and a base radius of 5 ft. How fast is the water level rising when the water is 6 ft. deep? (V=1/3 pi r^{2} h). Answered by Penny Nom. 





Pyramids and cones 
20060606 

From Melissa: I was wondering if a cone can be considered a pyramid. Looking at many definitions of pyramids I have read that pyramids come to a common vertex. A cone comes to a vertex. But I also read that pyramids all have triangular faces. In this case a cone would not be considered a pyramid. Am I correct? Answered by Chris Fisher. 





Surface areas 
20050511 

From Jessica: How can I demonstrate to my high school students the reason for the formulas for the surface area of a prism, right cylinder, and regular pyramid, and right cone? Answered by Penny Nom. 





Making a cone 
20031222 

From Tracie:
I am working on a craft project at home and I have been given the following information: 16" tall and 13" diameter at base, with 1 and 1/2 " opening at top.
Is there a basic formula for creating a cone with this info?
Answered by Claude Tardif and Penny Nom. 





A sphere inscribed in a cone 
20030810 

From A student: A sphere with radius 5cm is inscribed in a right circular cone 20 cm in height.find
(a) the base radius ,volume of the cone (b)volume of the shaded space( to 3 sig fig) Answered by Penny Nom. 





The vertex of a cone 
20030327 

From Holly: I read your response to Callie about whether a cone has a vertex or not. Is it ONLY a vertex if both halves of the cone are together or can one half of the illustration have a vertex? Answered by Walter Whiteley. 





A paper model of a cone 
20020814 

From Bruce: I have made a paper model of a cone, cut a sloping section, and removed the top. I have drawn the major and minor axis on the paper surface of the section. The major axis is not symmetrical about the minor axis. To me, this is not an ellipse. To me, an ellipse is a tubular section, because this gives a symmetrical major axis. What is your opinion? Answered by Walter Whiteley and Chris Fisher. 





Conics 
20020529 

From Brooke: Which conic cannot be generated by an intersection of a plane and a double napped cone? Answered by Chris Fisher. 





Bicycles and phone calls 
20010208 

From Sarah:
 A bicycle has a diameter of 66 centimeters. How many times must the tire rotate to travel 1 kilometer?explain answer.
 Becky want to make a long distance call to her friend Sarah from a pay telephone.She has $5.00 in change.The call costs $0.90 for the first three minutes and $0.24 for each additional minute.How long can Becky talk to Sarah?
Answered by Leeanne Boehm. 





Phone Number Possibilities 
20000109 

From Hamilton Weston: How do phone companies arrive at the possible number of phone numbers that can be generated for customers? Answered by Harley Weston. 





Nines and ones 
19991105 

From Greg Miller: Using the numbers 1, 1, 9, 9, only once each, how can I create an expression that equals 10 using only the basic functions of addition, subtraction, multiplication, division, and/or parentheses? Answered by Claude Tardif. 





Pay Phone Problem 
19980226 

From Shameq: Hi, I've been given a problem that I'm having some trouble with. I'd really appreciate any help. Here's the question (it's called the Pay Phone Problem) A pay phone will take only 10p, 20p, 50p, and £1 coins"(It's British). A woman has plenty of 10p and 20p coins. She has no other coins. She can put the coins into the pay phone in any order. INVESTIGATE the number of different ways, she could put the 10p and 20p coins into the pay phone. Answered by Penny Nom. 





Smith, Rodriguez and Jones 
19961107 

From Rafayel Ambartsumyan: On a train, Smith, Rodriguez, Jones are the fireman, brakeman, and engineer, but not in that order. Also aboard the train are three businessman who have the same names, a Mr. Smith, a Mr. Rodriguez, and a Mr. Jones. ..... Who is the engineer? Answered by Penny Nom. 

