Transum Software

Surface Area

Calculate the surface areas of the given basic solid shapes using standard formulae.

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This is level 7; Find the surface area of a variety of spheres. The diagrams are not to scale.

1

Find the surface area of a sphere with a radius of 7cm.
Give your answer to the nearest square centimetre.

Shape

cm2

2


Find the surface area of a sphere with a radius of 16cm.
Give your answer to the nearest square centimetre.


cm2

3


Find the surface area of a sphere with a radius of 43cm.
Give your answer to three significant figures.


cm2

4


Find the surface area of a sphere with a diameter of 114cm.
Give your answer to the nearest square centimetre.


cm2

5

Spaceship Earth, the icon of EPCOT in Florida, is a spectacular construction. Let's assume that it is a perfect sphere with a diameter of 50m. How many litres of paint would be needed to paint it if one litre covers 12 square metres. Round your answer up to the next whole number of litres.

Shape 5

cm2

6


The cross-section of a rubber ball has an outer diameter of 14 inches. The thickness of the rubber is 0.4 inches. What is the area of the inside surface of the ball to the nearest whole number of square inches?.


cm2

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This is Surface Area level 7. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 8 Level 9

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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An opportunity for students to write a computer program. There is nothing to download, all of the interaction takes place in the browser. Great for understanding angles and the properties of shapes.

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Description of Levels

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Level 1 - Find the surface area of shapes made up of cubes.

Level 2 - Find the surface area of a variety of cuboids.

Level 3 - Find the surface area of a variety of prisms.

Level 4 - Find the surface area of a variety of cylinders.

Level 5 - Find the surface area of a variety of cones.

Level 6 - Find the surface area of a variety of pyramids.

Level 7 - Find the surface area of a variety of spheres.

Level 8 - Find the surface area of composite shapes.

Level 9 - Mixed, more challenging questions involving surface area.

Volume - Find the volume of basic solid shapes.

Surface Area = Volume - Can you find the ten cuboids that have numerically equal volumes and surface areas? A challenge in using technology.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on 3D Shapes including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Surface Area Formulae

Cube: \(6s^2\) where \(s\) is the length of one edge.

Cuboid: \(2(lw + lh + wh)\) where \(l\) is the length, \(w\) is the width and \(h\) is the height of the cuboid.

Cylinder: \(2\pi rh + 2\pi r^2\) where \(h\) is the height (or length) of the cylinder and \(r\) is the radius of the circular end.

Cone: \(\pi r(r+l)\) where \(l\) is the distance from the apex to the rim of the circle (sloping height) of the cone and \(r\) is the radius of the circular base.

Cone: \(\pi r(r+\sqrt{h^2+r^2})\) where \(h\) is the height of the cone and \(r\) is the radius of the circular base.

Square based pyramid: \(s^2+2s\sqrt{\frac{s^2}{4}+h^2}\) where \(h\) is the height of the pyramid and \(s\) is the length of a side of the square base.

Rectangular based pyramid: \(lw+l\sqrt{\frac{w^2}{4}+h^2}+w\sqrt{\frac{l^2}{4}+h^2}\) where \(h\) is the height of the pyramid, \(l\) is the length of the base and \(w\) is the width of the base.

Sphere: \(4\pi r^2\) where \(r\) is the radius of the sphere.

Prism: Double the area of the cross section added to the product of the length and the perimeter of the cross section.

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