The formula for the volume of a pyramid is 1 3 × a r e a o f b a s e × h . Find the volume of a square-based pyramid with h = 6 c m .

Given, Volume of pyramid 1 3 × a r e a o f b a s e × h Height of the pyramid is 6 c m Base of the pyramid is in square shape. Area of square is a 2 Substitute the value of area of base and height in the formula. = 1 3 × a 2 × 6 = 2 a 2 Thus, the volume of the squared-based pyramid is 2 a 2 c m 3

Hero, a Greek mathematician , showed that the area A of a triangle with sides a , b and c can be found using the following formula: A = s s - a s - b s - c where s = 1 2 a + b + c Use Hero's formula to calculate the area of given triangle.

Given, Sides of triangle is 12 c m , 14 c m and 6 c m So, s = 1 2 a + b + c s = 1 2 12 + 14 + 6 s = 1 2 × 32 s = 16 Area of triangle = s s - a s - b s - c = 16 16 - 12 16 - 14 16 - 6 = 16 × 4 × 2 × 10 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 = 2 × 2 × 2 × 2 5 = 16 5 Thus, the area of triangle is 16 5 c m 2

Hero, a Greek mathematician , showed that the area A of a triangle with sides a , b and c can be found using the following formula: A = s s - a s - b s - c where s = 1 2 a + b + c Use Hero's formula to calculate the area of given triangle.

Given, Two sides of given triangle is equal. Sides of triangle is 12 . 3 c m , 18 . 6 c m and 18 . 6 c m So, s = 1 2 a + b + c s = 1 2 12 . 3 + 18 . 6 + 12 . 3 s = 1 2 × 43 . 2 s = 21 . 6 Area of triangle = s s - a s - b s - c = 21 . 6 21 . 6 - 12 . 3 21 . 6 - 18 . 6 21 . 6 - 12 . 3 = 21 . 6 × 9 . 3 × 3 × 9 . 3 = 3 × 3 × 3 × 2 × 2 × 0 . 2 × 9 . 3 × 3 × 9 . 3 = 3 × 3 × 2 × 9 . 3 0 . 2 = 167 . 4 0 . 2 Thus, the area of triangle is 167 . 4 0 . 2 c m 2

Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 2

Author:Michele Conway, Belle Cottingham, Alastair Duncombe & Amanda George

Michele Conway Mathematics Solutions for Exercise - Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 2

Attempt the free practice questions from Exercise 4: Exercise 2 with hints and solutions to strengthen your understanding. Cambridge Lower Secondary Maths Stage 9: Student's Book solutions are prepared by Experienced Embibe Experts.

Questions from Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 2 with Hints & Solutions

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 5

The formula for the volume of a pyramid is $\frac{1}{3} \times a r e a o f b a s e \times h$ . Find the volume of a square-based pyramid with $h = 6 c m$ .

Question Image

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 6

Pythagoras theorem uses the formula $c = \sqrt{a^{2} + b^{2}}$ . Pair the values of $a$ and $b$ with the matching of $c$ . $c$ has been rounded to $1 d . p .$

$a = 3.5, b = 4.5$	$a = 5, b = 12$	$a = 3, b = 4$	$a = 7, b = 4.2$
$c = 5$	$c = 8.2$	$c = 5.7$	$c = 13$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 7

Use the formula $v^{2} = u^{2} - 2 a s$ and find that the given values of $v, u, a$ and $s$ can be substituted to satisfy the equation or not?

$v = 5, u = 4, a = 0.5$ and $s = 9$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 7

Use the formula $v^{2} = u^{2} - 2 a s$ and find that the given values of $v, u, a$ and $s$ can be substituted to satisfy the equation or not?

$v = 4, u = 5, a = 0.5$ and $s = - 9$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 7

Use the formula $v^{2} = u^{2} - 2 a s$ and find that the given values of $v, u, a$ and $s$ can be substituted to satisfy the equation? Explain your answer.

$v = 5, u = 4, a = - 0.5$ and $s = - 9$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 7

Use the formula $v^{2} = u^{2} - 2 a s$ and find that the given values of $v, u, a$ and $s$ can be substituted to satisfy the equation? Explain your answer.

$v = 5, u = 4, a = 0.5$ and $s = - 9$

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 8

Hero, a Greek mathematician , showed that the area $A$ of a triangle with sides $a, b$ and $c$ can be found using the following formula:

$A = \sqrt{s (s - a) (s - b) (s - c)}$ where $s = \frac{1}{2} (a + b + c)$

Use Hero's formula to calculate the area of given triangle.

Question Image

EASY

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 16 - Formulae>Exercise 2>Q 8

Hero, a Greek mathematician , showed that the area $A$ of a triangle with sides $a, b$ and $c$ can be found using the following formula:

$A = \sqrt{s (s - a) (s - b) (s - c)}$ where $s = \frac{1}{2} (a + b + c)$

Use Hero's formula to calculate the area of given triangle.

Question Image

Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 2

Michele Conway Mathematics Solutions for Exercise - Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 2

Questions from Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 4: Exercise 2 with Hints & Solutions

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