Area and Surface Area

Area, SMB-036

Find the surface area of the solid pictured below which is composed of a right cone with a hemisphere attached to the base. Give your answer to the nearest square centimetre. (3 marks)

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Area, SMB-018

A right cone with perpendicular height of 8 cm, slant height of 10 cm and a base diameter of 12 cm is pictured below.

Find the total surface area of the cone, including its base, correct to two decimal places. (3 marks)

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Area, SMB-017

A square pyramid with a slant height of 15 centimetres is pictured below.

Find the total surface area of the pyramid, including its base. (2 marks)

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Area, SMB-016

A square pyramid with a perpendicular height of 8 metres is pictured below.

Using Pythagoras, calculate the slant height of the pyramid. (2 marks)

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Find the total surface area of the pyramid, including its base, to the nearest square metre. (2 marks)

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ii.

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ii.

Area, SMB-015

A letterbox, which has been constructed by joining a half cylinder and rectangular prism, needs to be painted on each external surface.

Find the surface area of the letterbox, giving your answer correct to the nearest square centimetre. (3 marks)

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Area, SMB-014

Calculate the surface area of the half-cylinder below (including the base), giving your answer correct to two decimal places. (3 marks)

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Area, SMB-013

Calculate the surface area of the cylinder below, giving your answer correct to two decimal places. (2 marks)

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Area, SMB-035

The surface area of a brick is given by the rule:

total surface area = 2 × [(width × height) + (width × length) + (height × length)]

The brick shown has a total surface area of 982 square centimetres.

What is the width of the brick? (2 marks)

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Area, SMB-034

The total surface area of a cube is 150 cm².

How long is an edge of the cube? (2 marks)

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Area, SMB-033

The rectangular prism, shown below, is cut in half to form 2 equal cubes.

What is the ratio of the surface area of the rectangular prism to one of the cubes? (3 marks)

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Area, SMB-032

A net of a cube is pictured below.

The cube has a volume of 512 cubic centimetres.

What is the height of the net in centimetres? (3 marks)

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Area, SMB-031

A target is drawn as follows

What is the area of the entire target?

Round your answer to the nearest square centimetre. (2 marks)

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Area, SMB-030

A glass aviary is made up of four triangles and a square, as shown in the diagram below.

Harry is hired to clean the interior sides of the aviary, not including the floor.

What is the area that Harry will need to clean? (2 marks)

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Area, SMB-029 MC

The plan of a square area of land is drawn below.

A mining licence is granted over part of the land.

All measurements are given in kilometres.

The area of land the mining licence covers is

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Area, SMB-027

Kate owns a farm with a square paddock. She increases the area of the paddock by changing it into the shape of trapezium.

What is the area of the new paddock, in square metres? (2 marks)

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$²$

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	$²$

Area, SMB-026

Clancy needs to paint all sides of a triangular prism.

The area of each triangular face is 12 cm².

What is the total area Clancy needs to paint? (2 marks)

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$²$

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	$²$

Area, SMB-025

An irregular shaped lawn is pictured below, with all measurements in metres.

What is the area of the lawn in square metres? (3 marks)

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$²$


	$²$

Area, SMB-024

A plan of Zev's backyard is shown.

Zev wants to fertilise the lawn in his backyard and needs to know the total area.

What is the total area of Zev's lawn, in square metres? (2 marks)

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$²$

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	$²$

Area, SMB-023 MC

Harry has an irregularly shaped back yard.

What is the area of Harry's back yard?

$²$
$²$
$²$
$²$

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	$²$

Area, SMB-022

A cube has a side length of 6 cm.

Two smaller cubes of side length 3 cm are attached to the larger cube as shown in the diagram below.

What is the surface area of the new object? (3 marks)

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$²$

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$²$


	$²$

Area, SMB-021 MC

Pablo cuts a square out of a rectangular piece of paper, as shown below.

The square Pablo cut out has a side length of 6 cm.

Which of these expressions gives the area of Pablo's piece of paper after cutting out the square?

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Area, SMB-020

A trapezium is constructed on a grid of 10 rectangles.

Each rectangle measures 3 cm × 7 cm.

Find the area of the trapezium? (2 marks)

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$²$

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	$²$




	$²$

Area, SMB-019 MC

Olive drew this plan of her lawn.

Which expression gives the area of Olive's lawn?

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Area, SMB-012

Find the surface area of the solid below where all measurements are in metres. (2 marks)

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Area, SMB-011

A triangular prism has the following dimensions (all measurements are in metres).

Draw a net of the solid (1 mark)

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Find the surface area of the prism. (2 marks)

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ii.

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ii.

Area, SMB-010

A triangular prism has the following dimensions (all measurements are in centimetres).

Draw a net for this solid. (1 mark)

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Find the surface area of the prism. (2 marks)

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ii.

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ii.

Area, SMB-009

Find the surface area of the rectangular prism pictured below, correct to 1 decimal place. All measurements are in metres. (2 marks)

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Area, SMB-008

Find the surface area of the rectangular prism pictured below. All measurements are in metres. (2 marks)

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Area, SMB-007

The diagram shows the shape of Carmel’s garden bed. All measurements are in metres.

Show that the area of the garden bed is 57 square metres. (2 marks)

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	$²$


	$²$


	$²$

Area, SMB-001

Find the area of the shaded part in the diagram below, giving your answer in square metres to 1 decimal place. (3 marks)

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Area, SMB-008 MC

Four identical circles of radius are drawn inside a square, as shown in the diagram below

The region enclosed by the circles has been shaded in the diagram.

The shaded area can be found using

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Area, SMB-006

A child's toy has the following design.

Find the area of the shaded region to the nearest square centimetre. (3 marks)

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$²$

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	$²$

Area, SMB-005

A path 1.5 metres wide surrounds a circular lawn of radius 3 metres.

Find the area of the path, correct to the nearest square metre. (2 marks)

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$²$

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$² ²$

Area, SMB-004

The diagram shows the floor of a shower. The drain in the floor is a circle with a diameter of 10 cm.

Find the area of the shower floor, excluding the drain, to the nearest square centimetre. (3 marks)

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$²$

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	$²$
	$² ²$

Area, SMB-003

The shaded region shows a quadrant with a rectangle removed.

Find the area of the shaded region, to the nearest cm². (2 marks)

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$²$

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	$²$

Area, SMB-002

What is the area of the shaded part of this quadrant, to the nearest square centimetre? (3 marks)

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$²$

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	$²$
	$² ²$

Measurement, STD2 M1 2022 HSC 34

A composite solid is shown. The top section is a cylinder with a height of 3 cm and a diameter of 4 cm. The bottom section is a hemisphere with a diameter of 6 cm. The cylinder is centred on the flat surface of the hemisphere.

Find the total surface area of the composite solid in cm², correct to 1 decimal place. (4 marks)

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♦ Mean mark 50%.

Measurement, STD2 M1 2020 HSC 25

A composite solid consists of a triangular prism which fits exactly on top of a cube, as shown.

Find the surface area of the composite solid. (3 marks)

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Measurement, STD2 M1 2018 HSC 27c

A shade shelter is to be constructed in the shape of half a cylinder with open ends. The diameter is 3.8 m and the length is 10 m.

The curved roof is to be made of plastic sheeting.

What area of plastic sheeting is required, to the nearest m²? (2 marks)

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$² ²$

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	$² ²$

Measurement, STD2 M1 2017 HSC 25 MC

In the circle, centre , the area of the quadrant is 100 cm².

What is the arc length , correct to one decimal place?

8.9 cm
11.3 cm
17.7 cm
25.1 cm

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♦ Mean mark 44%.

Area, SMB-028

What is the area of the shaded part of the figure? (2 marks)

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Measurement, STD2 M1 2016 HSC 30c

A school playground consists of part of a circle, with centre , and a rectangle as shown in the diagram. The radius of the circle is 45 m, the width of the rectangle is 20 m and is 100°.

What is the area of the whole playground, correct to the nearest square metre? (5 marks)

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$² ²$

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$²$


	$²$

$²$

$² ²$

Measurement, STD2 M1 2016 HSC 26a

Calculate the surface area of a sphere with a radius of 5 cm, correct to the nearest whole number. (1 mark)

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$²$

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	$² ²$

Measurement, STD2 M1 2008 HSC 2 MC

What is the surface area of the open box?

10 cm²
30 cm²
52 cm²
62 cm²

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$²$

Measurement, STD2 M1 2014 HSC 25 MC

A grain silo is made up of a cylinder with a hemisphere (half a sphere) on top. The outside of the silo is to be painted.

What is the area to be painted?

$²$
$²$
$²$
$²$

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$½$

♦ Mean mark 40%

$½$


	$²$

Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a terrace which is to be tiled.

Find the area of the terrace. (2 marks)

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Tiles are sold in boxes. Each box holds one square metre of tiles and costs $55. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

Find the total cost of the boxes of tiles required for the terrace. (2 marks)

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i. $²$

ii.

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	$²$

ii.
		$²$

Measurement, STD2 M1 2013 HSC 19 MC

A logo is designed using half of an annulus.

What is the area of the logo, to the nearest cm²?

$²$
$²$
$²$
$²$

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	$² ²$