# 1.4.1 Try some yourself

## Activity 8

If a litre is one cubic decimetre, how many litres are there in a cubic metre?

### Answer

Since a litre is one cubic decimeter, the question is asking how may cubic decimetres are in a cubic metre.

1 metre = 10 decimetres

so 1 m^{3} = 10^{3} cubic decimetres.

Hence there are 1000 litres in a cubic metre.

## Activity 9

Find the following without using your calculator, as an estimate for the calculator work in the next question.

(a) (

^{−}1)^{3}(b) 3

^{3}(c) 100

^{3}(d) 0.1

^{3}

### Answer

(a) (

^{−}1)^{3}=^{−}1 ×^{−}1 ×^{−}1 = 1 ×^{−}1 =^{−}1(b) 3

^{3}= 3 × 3 × 3 = 9 × 3 = 27(c) 100

^{3}= 100 × 100 × 100 = 10 000 × 100 = 1000 000 (a million)(d)

## Activity 10

Use your calculator to find the following.

(a) (

^{−}1.2)^{3}(b) 3.3

^{3}(c) 101

^{3}(d) 0.121

^{3}

### Answer

(a) Estimate: (

^{−}1)^{3}=^{−}1.Calculate: (

^{−}1.2)^{3}=^{−}1.728.(b) Estimate: 3

^{3}= 27.Calculate: 3.3

^{3}= 35.937.(c) Estimate: 100

^{3}= 1000 000.Calculate: 101

^{3}= 1030 301.(d) Estimate: .1

^{3}= .001.Calculate: 0.121

^{3}= 0.00177 (3 s.f.)

## Activity 11

What are the following?

(a)

(b)

### Answer

(a) = 1 since 1

^{3}= 1.(b) = 10 since 10

^{3}= 1000.

## Activity 12

Find the volume of a one-foot cube in cubic metres (1 foot = 30.48 cm). Estimate your answer first. Round your answer to three decimal places.

### Answer

To estimate an answer, choose a simple approximation, say

1 foot 30 cm = 0.3 m.

Then 1 foot cubed (0.3)^{3} = 0.027 m^{3}.

More accurately, 1 foot = 30.48 cm = 0.3048 m.

So 1 foot cubed = (0.3048)^{3} = 0.028 m^{3} to three d.p.

## Activity 13

Without using your calculator, find the following, as estimates for the calculator work in Question 7.

(a) 9

^{2}(b) 4

^{3}(c)

(d)

(e) (

^{−}3)^{2}

### Answer

(a) 9

^{2}= 9 × 9 = 81(b) 4

^{3}= 4 × 4 × 4 = 16 × 4 = 64(c) = 8 (since 8

^{2}= 64)(d)

(e) (

^{−}3)^{2}=^{−}3 ×^{−}3 = 9

## Activity 14

Use your calculator to find:

(a) 9.42

^{2}(b) 3.65

^{3}(c)

(d) 0.33

^{3}(e) (

^{−}2.713)^{2}

Use your answers to the previous question as rough checks. Round your answers to four decimal places.

### Answer

(a) 9.42

^{2}= 88.7364(b) 3.65

^{3}48.6271(c) 8.3666

(d) 0.33

^{3}0.0359 (check this by calculating , the estimate from 3(d) above, as a decimal.(e) (

^{−}2.713)^{2}7.3604 (N.B. To get this answer on a calculator, remember the brackets.)