Surface Area And Volume Revision Questions

Surface Area and Volume 2016 Sample Question 4 / 2013 Question 7 A greenhouse is built in the shape of a trapezoidal prism, as shown in the diagram above. The crosssection of the greenhouse (shaded) is an isosceles trapezium. The parallel sides of this trapezium are 4 m and 10 m respectively. The two equal sides are each 5 m. The length of the greenhouse is 12 m. The five exterior surfaces of the greenhouse, not including the base, are made of glass. The total area of the glass surfaces of the greenhouse, in square metres, is A. 196

B. 212

C. 224

D. 344

E. 672

2016 Question 5 A water tank in the shape of a cylinder with a hemispherical top is shown below. The volume of water that this tank can hold, in cubic metres, is closest to A. 80

B. 88

C. 96

D. 105

E. 121

2016 Question 1 A golf ball is spherical in shape and has a radius of 21.4 mm, as shown in the diagram below. Assume that the surface of the golf ball is smooth. a. What is the surface area of the golf ball shown? Round your answer to the nearest square millimetre. 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ b. Golf balls are sold in a rectangular box that contains five identical golf balls, as shown in the diagram below. What is the minimum length, in millimetres, of the box? 1 mark

____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________

2017 NHT Question 4 Paula has built a model house using a triangular prism on top of a rectangular box. The dimensions of the model house are shown on the diagram below. Paula will paint the outside walls and the roof of the model house. The area that will be painted, in square centimetres, is closest to A. 12 600 B. 26 400 C. 36 400 D. 37 700 E. 39 000 2017 NHT Question 4 Milk is made into cheese in the manufacturing building. There are two sizes of cheese, each made in the shape of a cylinder and of equal height. A small cylinder of cheese has a radius of 55 mm and a large cylinder of cheese has a radius of 75 mm.

b. A large cylinder of cheese is cut into five equal pieces and one piece is removed, as shown above. The area of sector 𝑂𝐴𝐵 (shaded) is 3534.3 mm . The total surface area of this piece is 12 200 mm . What is the height, ℎ, of this piece? Round your answer to the nearest millimetre. 2 marks ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ 2017 Question 4 A grain storage silo in the shape of a cylinder with a conical top is shown in the diagram below. The volume of this silo, in cubic metres, is closest to A. 550

B. 1304 C. 1327 D. 1398 E. 2560

2017 Question 1

2017 Question 1 Miki is planning a gap year in Japan. She will store some of her belongings in a small storage box while she is away. This small storage box is in the shape of a rectangular prism. The diagram below shows that the dimensions of the small storage box are 40 cm × 19 cm × 32 cm. The lid of the small storage box is labelled on the diagram above. a. i. What is the surface area of the lid, in square centimetres? 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ii. What is the total outside surface area of this storage box, including the lid and base, in square centimetres? 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ 2018 NHT Question 5 A square-based pyramid is shown in the diagram below. The base lengths of this pyramid are 20 cm. The slant edges of this pyramid are 20 cm. Which one of the following calculations gives the volume of this pyramid in cubic centimetres? 1 𝐀. ⎯⎯× 20 × 20 × 20 3 1   ⎯⎯ 𝐃. ⎯⎯× 20 × 20 × 10 × √2 3

1   ⎯⎯ 𝐁. ⎯⎯× 10 × 10 × 10 × √2 3 1   ⎯⎯ 𝐄. ⎯⎯× 20 × 20 × 20 × √2 3

1   ⎯⎯ 𝐂. ⎯⎯× 10 × 10 × 20 × √2 3

2018 NHT Question 7 A cylindrical fuel tank is shown in the diagram below. The radius of the fuel tank is 0.8 m. The length of the fuel tank is 3.8 m. The depth of fuel in the tank is 1.2 m. One thousand litres of fuel has a volume of 1 m . The amount of fuel in this tank is closest to A. 5094 litres. B. 5730 litres. C. 6147 litres. D. 6587 litres. E. 7420 litres.

2018 NHT Question 1 Shannon is a baker. One of her baking tins has a rectangular base of length 28 cm and width 20 cm. The height of this baking tin is 5 cm, as shown in the diagram below. a. What is the volume of this tin, in cubic centimetres? 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ Another baking tin has a circular base with a radius of 12 cm. The height of this baking tin is 8 cm, as shown in the diagram below. b. Shannon needs to cover the inside of both the base and side of this tin with baking paper. What is the area of baking paper required, in square centimetres? Round your answer to one decimal place. 2 marks ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ A cake cooked in the circular baking tin is cut into 10 pieces of equal size, as shown in the diagram below. The angle 𝜃 is also shown on the diagram. The angle 𝜃 is equal to 36°. d. What is the volume, in cubic centimetres, of one piece of cake? Round your answer to one decimal place. 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________

2018 Question 8

2018 Question 8 A cone with a radius of 2.5 cm is shown in the diagram below. The slant edge, 𝑥, of this cone is also shown. The volume of this cone is 36 cm . The surface area of this cone, including the base, can be found using the rule 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 = 𝜋𝑟(𝑟 + 𝑥). The total surface area of this cone, including the base, in square centimetres, is closest to A. 20

B. 42

C. 63

D. 67

E. 90

2018 Question 1 Tennis balls are packaged in cylindrical containers. Frank purchases a container of tennis balls that holds three standard tennis balls, stacked one on top of the other. This container has a radius of 3.4 cm and a height of 20.4 cm, as shown in the diagram below. The diameter of this container is 6.4 cm. b. What is the total outside surface area of this container, including both ends? Write your answer in square centimetres, rounded to one decimal place. 1 mark _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ A standard tennis ball is spherical in shape with a radius of 3.4 cm. c. i. Write a calculation that shows that the volume, rounded to one decimal place, of one standard tennis ball is 164.6 cm . 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ii. Write a calculation that shows that the volume, rounded to one decimal place, of the cylindrical container that can hold three standard tennis balls is 740.9 cm . 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ iii. How much unused volume, in cubic centimetres, surrounds the tennis balls in this container? Round your answer to the nearest whole number. 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________

2019 Question 3

2019 Question 3 An ice cream dessert is in the shape of a hemisphere. The dessert has a radius of 5 cm. The top and the base of the dessert are covered in chocolate. The total surface area, in square centimetres, that is covered in chocolate is closest to A. 52

B. 157

C. 236

D. 314

E. 942

2019 Question 7 A can of dog food is in the shape of a cylinder. The can has a circumference of 18.85 cm and a volume of 311 cm . The height of the can, in centimetres, is closest to A. 2.8

B. 3.0

C. 6.0

D. 11.0 E. 16.5

2019 Question 1 Each shipping container is in the shape of a rectangular prism. Each shipping container has a height of 2.6 m, a width of 2.4 m and a length of 6 m, as shown in the diagram below. b. What is the volume, in cubic metres, of one shipping container? 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ c. What is the total surface area, in square metres, of the outside of one shipping container? 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ d. One shipping container is used to carry barrels. Each barrel is in the shape of a cylinder. Each barrel is 1.25 m high and has a diameter of 0.73 m, as shown in the diagram below. Each barrel must remain upright in the shipping container. What is the maximum number of barrels that can fit in one shipping container? 1 mark ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________