Mathematical Topic: Geometry and Measures

CCS Container

Post date 29 September 2021

Carbon capture and storage is method of removing carbon dioxide from the atmosphere and storing it as a liquid underground. Carbon capture and storage is one possible method of slowing climate change.

Throughout this question you may ignore the mass of the container and consider only the mass of the liquid carbon dioxide that it contains. The liquid carbon dioxide is stored in a cylindrical container of volume 3.8m³.

a) The density of liquid carbon dioxide is 1100kg/m³.

Work out the mass of the liquid carbon dioxide.

[2 marks]

The 3.8m³ cylinder container of liquid carbon dioxide has a base of radius 0.5m.

b) Work out the height of the cylinder. Give your answer to 3 significant figures.

[2 marks]

A New Power Station

Post date 29 September 2021

A new kind of gas-fired power station releases on average 1.73×10⁴ kg of pure carbon dioxide (CO₂) every day. It also uses the heat of exhaust gases to provide community heating so the carbon dioxide leaving the power station is at same temperature as the environment. The density of CO₂ as it leaves the power station is 1.98 kg/m³.

a) What volume of pure CO₂will be emitted from the power station each day?

[2 marks]

The CO₂now enters the atmosphere and is ‘diluted’ by other air molecules and therefore occupies a larger volume. In the atmosphere, for every million (1000000) air molecules, there are 400 CO₂ molecules.

b) Work out the volume that the diluted CO₂will now take up in the atmosphere. Give your answer to 3sf.

[2 marks]

A new technology is added to the power station to capture this carbon dioxide and store it as a liquid.

c) The density of liquid carbon dioxide is 1100kg/m³.

Work out the volume that the amount carbon dioxide produced every day will occupy if stored as a liquid.

[2 marks]

A depleted oil field contains a reservoir of area 1150 m² which is 150m deep. This reservoir could be used to store the liquid carbon dioxide.

d) Evaluate how many years’ worth of carbon dioxide emitted from the power station could be stored in this oil field. Give your answer to two significant figures.

[3 marks]

Solar Panelling a House

Post date 29 September 2021

A homeowner wishes to cover their roof with solar panels.

Their roof can be modelled as a prism with volume 24m³

The height of the triangular cross section is h.

If solar panels can only be placed on the 2 rectangular sections of the roof

a) Work out the area of roof that could be covered by solar panels. Give your answer to 2.s.f.

[4 marks]

A company provides solar panels that are 1.5m long and 1.0m high and cost £200 each, including installation.

b) If this is the only size of solar panels available, how much will it cost the homeowner to buy and install them?

[3 marks]

An Offshore Wind Farm

Post date 29 September 2021

Below is a diagram of 3 offshore wind turbines, A, B and C, in a wind farm, as seen from above.

Given that the bearing from turbine C to turbine B is 90˚, and the distance from turbine A to turbine B is 3 km

Calculate the distances AC and CB.

[4 marks]

Allotment Areas

Post date 6 August 2021

A citizen wants to reduce their carbon footprint, so decides to grow their own produce in their garden.
The area set out for growing vegetables is shown below, and they want to place a shed in the area marked A.

Given that all dimensions are given in metres, and the total area of the plot is 65㎡ , find the values of \(x \) and \(y \) and hence the depth and width of the shed that they need to purchase.

[6 marks]

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