Review: circle and solids

Circle and solids, grade 8 Lesson 7 of 7Practice

Review: circle and solids

1

A round pool is 8 m across.
Find ( $\displaystyle \pi\approx3.14$ ):

a

the length of the fence around the pool, in metres

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

the area of a cover over the whole pool, in m²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

2

A round flower bed’s radius is 10 m.
A path 2 m wide was laid around it.
What is the path’s area? ( $\displaystyle \pi\approx3.14$ )

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

3

A car wheel is 60 cm across.
How many turns does the wheel make in a drive of 1.884 km? ( $\displaystyle \pi\approx3.14$ )

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

4

A candle is a cylinder of radius 3 cm and height 10 cm.
Find ( $\displaystyle \pi\approx3.14$ ):

a

how many cm³ of wax the candle has

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

how many cm² of paper it takes to wrap the candle around, without the bases

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

5

A traffic cone is a cone of radius 15 cm and height 36 cm.
Find ( $\displaystyle \pi\approx3.14$ ):

a

its slant height, in cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

b

its curved surface area, in cm²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

6

A container in the shape of a cylinder, of radius 50 cm, holds 157 litres.
How high is the container, in cm?
Write an equation and solve it (1 litre = 1000 cm³, $\displaystyle \pi\approx3.14$ ).

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

7

An aquarium is a box.
Its base is a rectangle 16 cm by 12 cm.
It is 15 cm high.
How long is the longest rod that fits inside it?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

8

The base’s side of a square pyramid is 16 m, and its height is 15 m.
What is the height of a side face, in metres?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

9

Two vessels:

a cylinder of radius 3 cm and height 4 cm;
a cone of radius 6 cm and height 3 cm.

Which vessel holds more? Write both volumes with $\displaystyle \pi$ .

Formulas: circle and solids, grade 8

The circle and the disc

The number pi – the value to calculate with
$\displaystyle \pi\approx3.14$
The circumference of a circle – $\displaystyle d$ the diameter
$\displaystyle C$ $\displaystyle =$ $\displaystyle \pi d$
The circumference of a circle – $\displaystyle r$ the radius
$\displaystyle C$ $\displaystyle =$ $\displaystyle 2\pi r$
The area of a disc
$\displaystyle A$ $\displaystyle =$ $\displaystyle \pi r^2$

The cylinder

The curved surface area – $\displaystyle r$ the radius of the base, $\displaystyle h$ the height
$\displaystyle L$ $\displaystyle =$ $\displaystyle 2\pi r h$
The surface area – the two bases and the curved surface
$\displaystyle A$ $\displaystyle =$ $\displaystyle 2\pi r^2+2\pi r h$
The volume – the base area times the height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \pi r^2 h$

The cone

The slant height $\displaystyle l$ – the hypotenuse of a triangle whose legs are the radius $\displaystyle r$ and the height $\displaystyle h$
$\displaystyle l^2$ $\displaystyle =$ $\displaystyle r^2+h^2$
The curved surface area
$\displaystyle L$ $\displaystyle =$ $\displaystyle \pi r l$
The surface area – the base and the curved surface
$\displaystyle A$ $\displaystyle =$ $\displaystyle \pi r^2+\pi r l$
The volume – a third of the cylinder with the same base and height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \frac{\pi r^2 h}{3}$

Pythagoras' theorem in space

The diagonal of a box $\displaystyle d$ – $\displaystyle a$ , $\displaystyle b$ , $\displaystyle c$ its three edges
$\displaystyle d^2$ $\displaystyle =$ $\displaystyle a^2+b^2+c^2$
In a square pyramid – $\displaystyle k$ the height of a side face, $\displaystyle h$ the pyramid’s height, $\displaystyle a$ the side of the base
$\displaystyle k^2$ $\displaystyle =$ $\displaystyle h^2+\left(\frac{a}{2}\right)^2$