Review: measures and solids

Measures and solids, grade 6 Lesson 16 of 16Practice

Review: measures and solids

1

Calculate.

a

3.2 km in metres

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b

450 g in kg

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c

2 m² in cm²

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d

3500 cm³ in litres

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2

How many faces, edges and vertices does each solid have?

a cube;
a prism whose base is a triangle;
a pyramid whose base is a square.

3

In a cylinder’s net the curved surface is a rectangle, and one of its sides goes exactly once around the base.
The base’s radius is 5 cm.
How long is that side? ( $\displaystyle \pi\approx3.14$ )

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4

A disc is 12 cm across.
Calculate ( $\displaystyle \pi\approx3.14$ ):

a

its circumference, in cm

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/ – 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 area, in cm²

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5

A round table’s circumference is 251.2 cm.
What is its diameter? ( $\displaystyle \pi\approx3.14$ )

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6

A rug is shaped like half a disc.
Its diameter is 2 m.
What is the rug’s area, in m²? ( $\displaystyle \pi\approx3.14$ )

/ – 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

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7

A pool is a box 10 m long, 5 m wide and 1.2 m deep.
How many m³ of water does it hold?
And how many litres?

In m³

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In litres

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8

A can is a cylinder: its radius is 3 cm, its height 12 cm.
The label says 330 ml.
Does the drink fit in it? ( $\displaystyle \pi\approx3.14$ )
Explain.

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9

A pyramid and a prism have the same base and the same height.
The prism’s volume is 90 cm³.
What is the pyramid’s volume?

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10

A field is made of a 40 m by 20 m rectangle.
At each of its short ends there is a half disc 20 m across.
What is the field’s perimeter?
And its area? ( $\displaystyle \pi\approx3.14$ )

The perimeter

/ – 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

The area

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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
$\displaystyle V$ $\displaystyle =$ $\displaystyle \frac{2}{3}\times\pi r^2\times2r$