Volume And Surface Area Of Shapes

Question 1

Volume of Prism

Answer 1

Area of Cross Section x Length

Question 2

Volume of Triangular Prism

Answer 2

1/2 Base x Height x Length

Question 3

Volume of Cylinder

Answer 3

π Radius^2 x Height

Question 4

Surface Area of a Cylinder

Answer 4

2π x Radius^2 + 2π x Radius x Height

Question 5

Volume of a Sphere

Answer 5

4/3 πr^3

Question 6

Surface Area of a Sphere

Answer 6

4π r^2

Question 7

Volume of a Hemi-Sphere

Answer 7

2/3π r^3

Question 8

Surface Area of a Hemi-Sphere

Answer 8

2π r^2 + πr^2

or

3π r^2

Question 9

Volume of a Square Based Pyramid

Answer 9

1/3 x Area of Base x Height

Question 10

Volume of a Cone

Answer 10

1/3 Area of Base x Height (1/3π r^2h)

Question 11

Surface Area of a Cone

Answer 11

πr^2 + π rl

l = slanting length/height of cone

Question 12

Volume of a Frustum

Answer 12

1/3π R^2 H - 1/3π r^2 h

(R = Bottom Radius
H = What would be full height of Cone from Bottom of Frustum)

(r = Top Radius
h = What would be the height between top of Frustum and top of cone)

Question 13

Diameter of a Circle (or a sector)

Answer 13

π x d
or
2 x π x r

(For sector, put the ‘angle of the sector/360’ at the start)

Question 14

Area of a Circle (or a sector)

Answer 14

π x r^2

For sector, put the ‘angle of the sector/360’ at the start

Question 15

The Formula to work out the area of any triangle

Answer 15

1/2 ab sin(c)