Worksheets for GCSE Mathematics. Volume and Surface Area. mr-mathematics.com Maths Resources for Teachers. Shape
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1 Worksheets for GCSE Mathematics Volume and Surface Area mr-mathematics.com Maths Resources for Teachers Shape
2 Volume & Surface Area Worksheets Contents Differentiated Independent Learning Worksheets Volume of Prisms Total Surface Area of Prisms Volume and Surface Area of Cylinders Volume and Surface Area of Pyramids Volume of a Cone Surface Area of a Cone Volume and Surface Area of Spheres Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 80 Solutions Volume of Prisms Total Surface Area of Prisms Volume and Surface Area of Cylinders Volume and Surface Area of Pyramids Volume of a Cone Surface Area of a Cone Volume and Surface Area of Spheres Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 150
3 Volume of Cuboids Q1. Calculate the volume of the following cuboids. a) c) d) Q2. Calculate the volume of this cuboid. Q3. a) 5 m 10 cm 5 m 5 m 4 cm 3 cm This box is made from 2 cm thick wood. How many 3 cm cubes will fit inside the box? How much space is left inside the box when the 3 cm 3 are arranged inside? 2.5 cm 5.8 m 4 cm 12 cm 2.4 m 2.4 m S S
4 Total Surface Area of Prisms Q1. Calculate the total surface area of these cuboids. a) c) d) Q2. Calculate the total surface area of the two shapes. Q m 12 cm 12.5 m 6.2 m 5 cm 5 cm Calculate the total surface area of the two shapes. 5.8 cm 7 cm 5.8 cm 5.8 cm 4 cm 6 cm S S
5 Cylinders Q1. For each of these cylinders calculate, i) the volume ii) the total surface area. Q2. a) a) c) d) This annulus has an outside diameter of 20 cm, an inside diameter of 15 cm and a depth of 45 cm. Calculate the volume of the annulus. S It is made out of a plastic that has a density of 9.2 g/cm 3. Calculate the mass of the annulus. Q3. Three solid congruent cylinders fit perfectly inside this cuboid as shown. Calculate the volume of the remaining space. S
6 Pyramids Q1. Calculate the volume and total surface area of the following pyramids. a) Q2. Calculate the volume and total surface area of the following pyramids. a) Q3. Calculate the volume of the two solids. S a) S
7 Q1. Calculate the volume of each solid. Volume of a Cone a) c) d) Q2. The cone and cylinder have equal volumes. Calculate the radius of the cylinder. Round your answer to three significant figures. S Q3. This sector is rolled to create the cone. Leaving both answers in terms of π, calculate: a) the curved surface area of the cone the volume of the cone. S
8 Surface Area of Cones Q1. Calculate the total surface area of each cone. Q2. Find the total surface area of the following cones. Give your answer in terms of π. a) Base radius = 3 cm, Perpendicular height = 5 cm. Base radius = 24 cm, Perpendicular height = 40 cm. c) Base diameter = 15 cm, Perpendicular height = 10 cm. Q3. Calculate the curved surface area from of the cones that are to be made from the following sectors. Leave your answers as a multiple of π. Q4. S S a) A cone has a curved surface area of 60 cm 2 and a slant length of 8 cm. Calculate the radius of the base. A cone has a curved surface area of 360 cm 2 and a base radius of 4 cm. Calculate the perpendicular height.
9 Spheres Q1. Calculate the volume and curved surface area of these spheres: a) c) Q2. Calculate the volume of these solids. a) Q3. Calculate the total surface area of this compound solid. S Q4. The sphere and the cone shown have the same volume. Calculate the height of the cone S
10 Solutions Volume of Cuboids Q1. a) 70 cm cm 3 c) 125 cm 3 d) cm 3 Q2. Volume = cm 3 Q3. a) 12 cubes 156 cm 3 S S
11 Total Surface Area of Prisms Solutions Q1. a) 290 cm cm 2 c) m 2 d) cm 2 Q2. a) 300 cm 2 66 cm 2 Q3. a) 632 cm cm 2 S S
12 Solutions Q1. a) i) Volume = cm 3 ii) Surface Area = cm 2 c) i) Volume = cm 3 ii) Surface Area = cm 2 Q2. a) Volume = cm 3 Mass = 56.9 kg Q3. Volume = cm 3 Cylinders i) Volume = cm3 ii) Surface Area = cm2 d) i) Volume = cm 3 ii) Surface Area = cm 2 S S
13 Solutions Q1. a) Volume = cm 3 Surface Area = cm 2 Pyramids Volume = cm 3 Surface Area = cm 2 Q2. a) Volume = cm 3 Volume = 127 cm 3 Q3. a) Volume = 780 cm 3 Volume = cm 3 S S
14 Solutions Q1. a) Volume = cm 3 c) Volume = cm 3 Q2. Radius = 5.66 cm Q3. a) Curved surface area = 4π cm 2 Volume of the cone = cm 3 Volume of a Cone Volume = cm 3 d) Volume = cm 3 S S
15 Solutions Q1. Q2. Surface Area of Cones a) cm cm 2 c) 52.2 cm 2 d) cm 2 e) 58.9 cm 2 f) 31.7 cm 2 a) TSA = 21π TSA = 1344π c) TSA = 150π Q3. a) CSA = 250 π CSA = 24π c) CSA = 8π 3 Q4. a) Radius = 2.39 cm Perpendicular Height = cm S S
16 Solutions Spheres Q1. Calculate the volume and curved surface area of these spheres: a) Volume = 418 cm 3 Surface Area = cm 2 Q2. Calculate the volume of these solids. a) Volume = 888 cm 3 Q3. Surface Area = cm 2 Q4. Height = 16 cm Volume = cm 3 Surface Area = cm 2 Volume = 94.3 cm 3 c) Volume = cm 3 Surface Area = cm 2 S S
Worksheets for GCSE Mathematics. Volume and Surface Area. Mr Black's Maths Resources for Teachers GCSE 1-9. Shape
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