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Surface Area

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

Level 1 Level 2 Level 3 Level 4 Volume Exam-Style Description Help More

This is level 4; Use a formula to find the surface area of standard solid shapes. The diagrams are not to scale.

Shape1 1. Find the surface area of this solid cylinder if the radius of the circular top is 41cm and its height is 44cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape2 2. Find the surface area of a solid cone if the radius of the circular base is 25cm and the length of the sloping side is 26cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape3 3. Find the surface area of a sphere with a diameter of 72cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape4 4. Find the surface area of a triangular prism if the area of its cross section is 51cm2, its length is 39cm and the 3 sides of the triangular ends add up to 33. cm2 Correct Wrong
Shape5 5. Find the surface area of a solid cylinder if the diameter of the circular end is 72cm and its length is 43cm. Give your answer to the nearest square centimetre. cm2 Correct Wrong
Shape6 6. Find the surface area of a square based pyramid if the length of a side of the square base is 10cm and the area of each triangular face is 52cm2. cm2 Correct Wrong
Shape7 7. The cross section of a prism is a right angled triangle as shown in the diagram. Calculate the surface area of the prism if AB = 10cm, BC = 18cm and CD = 24cm. cm2 Correct Wrong
Shape8 8. A cylindrical tube is used to store circular salted potatoe crisps. All if its external surface area except one of the circular ends is painted red. Calculate the area of the painted region if the length of the tube is 35cm and the diameter of the tube is 13cm. Give your answer to the nearest square centimetre.

cm2 Correct Wrong
Shape9 9. A sphere has a surface area of 100cm2. Calculate its radius in centimetres giving your answer to three significant figures. cm2 Correct Wrong
Shape10 10. The frame for a large tent is in the shape of an isosceles triangular prism. The height of the tent is 3.5m, the width of the tent (at the triangular ends) is 3.1m, the sloping edges of the tent are each 3.82m an the length of the tent is 6.1m. Calculate the area of canvas needed for the tent (excluding the bottom of the prism as that is where the ground sheet goes). Give your answer to the nearest integer.

cm2 Correct Wrong


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Description of Levels



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 cuboids and other composite shapes.

Level 4 - Use a formula to find the surface area of standard solid shapes.

Volume - Find the volume of basic solid shapes.

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).

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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.

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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