







The lateral side length of a cone 
20160605 

From Diane: Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm. Answered by Penny Nom. 





Maximize the volume of a cone 
20131009 

From Conlan: Hi I am dong calculus at school and I'm stumped by this question:
A cone has a slant length of 30cm. Calculate the height, h, of the cone
if the volume is to be a maximum.
If anyone can help me it would be greatly appreciated.
thanks. Answered by Penny Nom. 





A storage box with a slanted roof 
20120213 

From Sophia: Hi!
I have another problem.
The diagram shows a side view of a box which is used to store small logs of
wood for burning in a fire place. The slopping lid has an overhand of 15cm.
a) Calculate the total length of the slopping lid to the nearest cm.
b) When the lid is open above ground will the end of the lid be?
P.S. Please see attached. Answered by Penny Nom. 





Calibrating a conical tank 
20110205 

From Bill: Hi, I have a round tank with tapered sides where I know the diameter at the top and bottom. Is there a formula I can use to calculate the volume by measuring from the bottom up the side (at the angle of the side) to any given point? Thanks, Bill Answered by Stephen La Rocque and Penny Nom. 





The volume of a cone 
20081203 

From Tamriko: Hi! Help me, please to solve the following problem: The diameter of an icecream cone is 6 cm and the slant height is 10 cm. What volume of icecream would fit inside the cone? Thanks! Answered by Penny. 





Some angles in a pyramid 
20080804 

From Carla: A symmetrical pyramid stands on a square base of side 8cm. The slant height of
the pyramidis 20cm. Find the angle between the slant edge and the base, and the angle between
a slant face and the base. Answered by Penny Nom. 





Finding Angles in a Pyramid 
20080730 

From Carla: A pyramid has its vertex directly above the centre of its square base. The edges of the base
are each 8cm, and the vertical height is 10cm. Find the angle between the slant face and the base,
and the angle between the slant edge and the base. Answered by Janice Cotcher. 





The radius of a cone 
20070507 

From Braden: i need to find the surface area but i only have the slant height and the height i need the radius how do i find it? Answered by Penny Nom. 





Finding the vertical height of a roof 
20070305 

From Zainab: The question is: If the vertical height if a triangle is half the width of the base and the slant length is 6 metres, find the exact vertical height of this part of the roof. I'm actually confused about finding out the height of an equilateral triangle if you're only given the length or slant height. Please help! O.o Answered by Stephen La Rocque. 





A cone that is cut off at the top 
20020923 

From Stuart: I have to work out the dimensions and arcs of a cone that is cut off at the top. I.e Top diameter is 33mm to bottom diameter is 43mm and the depth is 80mm Are you able to work what the flat of this cone would be as I need to design within the flat area and then have it cut out. I really need to know what the flat of it is before it is cut and curled to form the above cone. Answered by Walter Whiteley. 





Slant height of a cone 
20000224 

From Jocelyn Wozney: I need help with this problem for my high school calculus class. Any help you can give me will be greatly appreciatedI am pretty stumped. "Express the volume of a cone in terms of the slant height 'e' and the semivertical angle 'x' and find the value of 'x' for which the volume is a maximum if 'e' is constant. Answered by Harley Weston. 

