Perimeter, Are and Volume

Question 1

Area of a circle - formula

Answer 1

Area = Pi x Radius squared

Question 2

Area of an annulus - formula

Answer 2

Area= Pi x ( Radius (large circle) Squared x radius squared )

Question 3

Area of a sector - formula

Answer 3

Area = Theta over 360 x Pi x Radius squared

Question 4

Area of a semicircle - formula

Answer 4

Area = 1/2 x Pi x Radius squared

Question 5

Area of a quadrant - formula

Answer 5

Area = 1/4 x Pi x Radius squared

Question 6

Area of composite shapes

Answer 6

1. Divide the composite shape into two or more plane shapes.
2. Calculate the area of each plane shape.
3. Add or subtract the areas of the plane shapes.
4. Write the answer to the specified level of accuracy with the correct units.

Question 7

Area of a trapezium - formula

Answer 7

Area = 1/2 x (a+b)h
= h over 2 (a+b)

Question 8

Trapezoidal rule

Answer 8

Area = h/2 (df + dt)

Question 9

Surface area of right prisms

Answer 9

1. Visualise the surfaces of the solid. If necessary draw the net of the solid.
2. Write a formula for the surface area, using the net as a guide.
3. Substitute the values into the formula for the surface area.
4. Use your calculator to find the surface area.
5. Write the answer to the specified level of accuracy with the correct units.

Question 10

Surface are of an open cylinder - formula

Answer 10

Surface Area = 2 x Pi x radius x height
Curved Surface = 2 x Pi x radius x height

Question 11

Surface are of a closed cylinder - formula

Answer 11

Surface Area = 2 x Pi x radius squared + 2 x Pi x radius x height
Area of top = Pi x radius squared
Area of bottom = Pi x radius squared
Curved surface = 2 x Pi x radius x height

Question 12

Surface area of sphere - formula

Answer 12

Surface Area = 4 time Pi x radius squared

Question 13

Surface area of open hemisphere - formula

Answer 13

Surface Area = 2 x Pi x radius squared

Question 14

Surface area of closed hemisphere - formula

Answer 14

Surface Area = 3 x Pi x radius squared
Area of curved surface = 2 x Pi x radius squared
Area of base = Pi x radius squared

Question 15

Surface area of a square pyramid

Answer 15

The surface area of a pyramid is found by finding the area of each face. For pyramids, the surface area is calculated by adding the area of the base and the area of the triangular faces. To find the area of the triangular face requires the slant height. The slant height of a right pyramid is the distance from the apex to the base, along a triangular face.

Question 16

Surface are of square pyramid - formula

Answer 16

SA=s2 +4×(1/2sl)

Question 17

Surface are of cone - formula

Answer 17

SA=πr2 +πrl

Question 18

Volume of cube - formula

Answer 18

V = Ah = (s2 ) × s = s3

Question 19

volume of rectangular prism - formula

Answer 19

V = Ah = lb × h = lbh

Question 20

Volume of triangular prism - formula

Answer 20

V= A H = ( 1/2 b h ) × H

Question 21

Volume of cylinder - formula

Answer 21

V = Ah = (πr2) × h = πr2h

Question 22

Volume of sphere - formula

Answer 22

V = 4/3 π r 3

Question 23

Volume of square pyramid - formula

Answer 23

V = 1/3 A h = 1/3 × s 2 × h

Question 24

Volume of rectangular pyramid - formula

Answer 24

V = 1/3 A h = 1/3 × l b × h

Question 25

Volume of cone - formula

Answer 25

V = 1/3 A h = 1/3 × π r 2 × h

Question 26

Capacity

Answer 26

The capacity of a container is the amount of liquid it
can hold. Some solids have both a volume and a capacity. For example, a can of soft drink is a cylinder that has a volume (V = πr 2h) and a capacity (360 mL). The base unit for capacity is the litre (L). Three commonly used units for capacity are the megalitre (ML), kilolitre (kL) and millilitre (mL).