Volume of Cylinders, Cones & Spheres — Drills
Volume of Cylinders, Cones & Spheres has 9 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 9 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Volume — Space inside, in cubic units.
- Factor — A number that divides evenly into another.
- Radius — Centre to edge. Half the diameter.
- Diameter — All the way across through the centre. d = 2r.
- Cylinder — Two parallel circles joined by a curved surface. V = π r2 h.
- Cone — A circle tapering to a point. V = 13π r2 h.
- Sphere — A ball. V = 43π r3.
- Height — The perpendicular distance from the base to the opposite corner.
Cylinder
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a cylinder with radius 6 and height 9, in terms of π.
Worked answer
324pi
π(6)2(9)
= 324π
Problem 2
Find the volume of a cylinder with radius 8 and height 7, in terms of π.
Worked answer
448pi
π(8)2(7)
= 448π
Cone
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a cone with radius 12 and height 11, in terms of π.
Worked answer
528pi
13π(144)(11)
= 1584π3
= 528π
Problem 2
Find the volume of a cone with radius 3 and height 9, in terms of π.
Worked answer
27pi
13π(9)(9)
= 81π3
= 27π
Sphere
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a sphere with radius 3, in terms of π.
Worked answer
36pi
33 = 27
43π(27) = 36π
Problem 2
Find the volume of a sphere with radius 6, in terms of π.
Worked answer
288pi
63 = 216
43π(216) = 288π
Radius
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cylinder has diameter 8 cm. What radius goes into the formula?
Worked answer
4
8 ÷ 2 = 4 cm
Problem 2
A cylinder has diameter 16 cm. What radius goes into the formula?
Worked answer
8
16 ÷ 2 = 8 cm
Decimal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the volume of a cylinder with radius 8 and height 8, rounded to one decimal place. Use π ≈ 3.14159.
Worked answer
1608.5
π(64)(8) = 512π
512 × 3.14159 ≈ 1608.5
Problem 2
Find the volume of a cylinder with radius 2 and height 6, rounded to one decimal place. Use π ≈ 3.14159.
Worked answer
75.4
π(4)(6) = 24π
24 × 3.14159 ≈ 75.4
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cylinder of height 7 has volume 63π. Find its radius.
Worked answer
3
π r2(7) = 63π
r2 = 9
r = 3
Problem 2
A cone with radius 5 has volume 50π. Find its height.
Worked answer
6
13π(25)h = 50π
25/3h ... multiply both sides by 3: 25h = 150
h = 6
Comparing
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cone and a cylinder have the same radius and the same height. The cone's volume is
- twice as much
- one third of the cylinder's
- the same
- three times as much
Worked answer
one third of the cylinder's
Cylinder: π r2 h
Cone: 13π r2 h
So one third.
Composite figures
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A silo is a cylinder of radius 3 and height 9, topped by a cone of the same radius and height 6. Find the total volume in terms of π.
Worked answer
99pi
Cylinder: π(9)(9) = 81π
Cone: 13π(9)(6) = 18π
81π + 18π = 99π
Problem 2
A silo is a cylinder of radius 6 and height 8, topped by a cone of the same radius and height 3. Find the total volume in terms of π.
Worked answer
324pi
Cylinder: π(36)(8) = 288π
Cone: 13π(36)(3) = 36π
288π + 36π = 324π
Scale
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A cylinder's height is multiplied by 3 and everything else stays the same. By what factor does the volume grow?
Worked answer
3
V = π r2 h
h appears once, so the volume scales by 3.
Factor 3
Problem 2
A cylinder's height is multiplied by 4 and everything else stays the same. By what factor does the volume grow?
Worked answer
4
V = π r2 h
h appears once, so the volume scales by 4.
Factor 4