Formulas
Variable calculations
Cuboids & Prims
Spheres, Cones, and Pyramid
General riddles
100
1L=xcm3 (10 secs)
find x
1000cm3
100
Calculate the volume of a cylinder if, r=4cm, h=10. (1:00min)
V=pi x 42 x 10
V=503cm3
100
A rectangular cuboid has sides 3 cm and 7 cm with a height of 8 cm find the volume of the cuboid.
V= s x s x h
V= 7 x 3 x 8
V = 168
100
The diameter of the sphere is 12 cm. Find the volume of the sphere
V=4/3 x pi x r3
V=4/3 x pi x 63
V=905 cm3
100
What has one eye, but cannot see?
A needle
200
What is the volume of a sphere? (15 sec)
V=4/3 x pi x r3
200
What is the volume of a cone if the diameter of the cone is 6 and the height is 10? (1:00min)
V=1/3 x pi x r2 x h
V=1/3 x pi x 32 x 10
V=94.2cm3
200
A right-angled triangular prism has a base of 12 cm, a height of 11 cm, and a length of 13 cm. Find its volume.
V=A x l
A=1/2 x 12 x 11
A=66cm2
V=66 x 13
V=858 cm3
200
The diameter of a cone is 6 cm and its height is 10 cm. Find the volume of the cone.
r=3 cm
V=1/3 x pi x r2 x h
V=1/3 x pi x 32 x 10
V=94.2 cm3
200
I am something you can't touch, but you can break.
A promise
300
What is the volume of a cylinder?(15 secs)
V=pi x r2 x h
300
Find the radius of a sphere if the volume of the sphere is 300cm3.(1:00 min)
r=cube root (300 x 3/4 x pi)
r=4.15 cm
300
When 3L of oil is removed from an upright cylindrical can, the level falls by 10 cm. Find the radius of the can.
3L=3000cm3
V=pi x r2 x h
r=square root(V/pi x h)
r=square root(V/pi x 10)
r=9.77cm
300
Find the volume of the pyramid if it has a square base of 0.13 m and a vertical height of 18cm.
V=1/3 (s x s) x h
V=1/3 (13 x 13) x 18
V=1014 cm3
300
The more I exist, the less you can see.
Darkness
400
If a cone is attached to a hemisphere, what formulas would be used to determine the volume
(1/3 x pi x r2 x h) + (2/3 x pi x r3)
400
Find the length of a cylinder of volume 3L and radius 30 cm. (1:30 min)
V/pi x r2 = h
3000/pi x 302 = h
h=1.06cm
400
For two cylinders A and B, the ratio of lengths are 3:1, and the ratio of diameters is 1:2. Calculate the ratio of their volumes.
400
An inverted cone of height 10 cm and base radius of 6.4 cm contains water to a depth of 5 cm, measured from the vertex. Calculate the volume of water in the cone.
r=3.2 cm h=5 cm
V=1/3 x pi x r2 x h
V=1/3 x pi x 3.22 x 5
V=53.6 cm3
400
There’s a one-story house in which everything is yellow. Yellow walls, yellow doors, yellow furniture. What color are the stairs?
There isn’t any—it’s a one-story house.
500
A cylinder is 'sandwiched' between a hemisphere and cone, what is the formula needed to solve the question? (45 sec)
V=(1/3 x pi x r2 x h) + (pi x r2 x h) + (2/3 x pi x r3)
500
A cube's side is 3 cm, the same cube has the same volume as a cylinder, which has a height of 10cm. Find the diameter of the cylinder. (2:30min)
Vol. of cube= 33= 27cm3
Vol of cylinder= pi x r2 x h
r=square root(27/pi x 10)
r=0.92
d=1.84
500
A business buys paint at $30,000 for 20 m3. It puts the paint in tins of capacity 0.8L and sells them at $5.95 each. Work out the profit (5 min)
500
The volume of the paint in a tube is 150 cm3. If this paint is squirted out in a straight line through a circular hole of diameter 5mm, how long will this line be?
d=5 mm
r=2.5 mm
r=0.025 cm
V=pi x r2 x h
150=pi x 0.0252 x h
150/0.0252=pi x h
2400/pi=h
h=764 cm
500
A hostage-taker kidnaps 20 people. He presents them with water and 2 pills, one of which is poisonous. The hostage-taker survives all 20 times. How was this possible?
The water is poisonous, not the pills