Practice: volumes

Measures and solids, grade 6 Lesson 15 of 16Practice

Practice: volumes

1

Find the volume ( $\displaystyle \pi\approx3.14$ ).

a

a box 8 cm by 5 cm by 2 cm; in cm³

/ – 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

a cube whose edge is 10 cm; in litres

/ – 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

c

a cylinder: radius 2 cm, height 5 cm; in cm³

/ – 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

d

a cone: radius 3 cm, height 4 cm; in cm³

/ – 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 box is 10 cm by 6 cm by 5 cm.
How many centimetre cubes fit in 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

3

A water tank is a cylinder: its radius is 50 cm, its height 1 m.
How many litres does it hold? ( $\displaystyle \pi\approx3.14$ )

/ – 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 chocolate bar is a prism lying on its side: its base is a triangle of 6 cm².
The bar’s length – the prism’s height – is 20 cm.
What is the bar’s volume?

/ – 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

Box A’s edges are 2 cm, 3 cm and 5 cm.
Each edge of box B is twice as long as the matching edge of box A.
How many times A’s volume is B’s?

/ – 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 glass is a cylinder: its radius is 4 cm, its height 10 cm.
How many full glasses can be poured from a 1.5-litre bottle? ( $\displaystyle \pi\approx3.14$ )
Explain.

7

A pit is dug in the shape of a box: 4 m by 3 m, 2 m deep.
The earth taken out is heaped into a pyramid whose base is a 6 m by 6 m square.
How high is the heap?

/ – 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

Dana says: “Two solids with the same volume always have the same surface area.”
Is she right?
Explain with an example.

Formulas: measures and solids, grade 6

The circle and the disc

The diameter $\displaystyle d$ is two radii $\displaystyle r$
$\displaystyle d$ $\displaystyle =$ $\displaystyle 2\times r$
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 – $\displaystyle r$ the radius
$\displaystyle A$ $\displaystyle =$ $\displaystyle \pi r^2$

Volumes

The volume of a box – $\displaystyle a$ the length, $\displaystyle b$ the width, $\displaystyle c$ the height
$\displaystyle V$ $\displaystyle =$ $\displaystyle a\times b\times c$
The volume of a box, a prism or a cylinder – $\displaystyle S$ the area of the base, $\displaystyle h$ the height
$\displaystyle V$ $\displaystyle =$ $\displaystyle S\times h$
The volume of a cylinder – $\displaystyle r$ the radius of the base, $\displaystyle h$ the height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \pi r^2 h$
The volume of a pyramid – a third of the prism with the same base and height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \frac{S\times h}{3}$
The volume of a cone – a third of the cylinder with the same base and height
$\displaystyle V$ $\displaystyle =$ $\displaystyle \frac{\pi r^2 h}{3}$
The volume of a sphere – two thirds of the cylinder around it
$\displaystyle V$ $\displaystyle =$ $\displaystyle \frac{2}{3}\times\pi r^2\times2r$