Question 1

A cylinder has radius 5 cm and height 12 cm. Find its volume (to 3 s.f.).

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Question 2

A sphere has radius 7 cm. Find its volume and surface area.

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Question 3

Find the distance between A(2.5, 3.5) and B(8.5, 11.5).

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Question 4

A surveyor places a point M at the midpoint of A(3, 12) and B(15, -4). Find the coordinates of M.

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Question 5

A cylinder has radius 3 cm and height 10 cm. Find its TOTAL surface area (closed).

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Question 6

A cone has radius 6 cm and vertical height 8 cm. Find its volume.

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Question 7

A rectangle has vertices at (1, 2), (7, 2), (7, 10), (1, 10). Find the length of the diagonal.

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Question 8

Find the distance between A(0, 5, 12) and B(0, 0, 0).

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Question 9

Two coordinates A(2, 4) and B(2, 10) are on a vertical line. Find the distance.

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Question 10

Find the distance from the origin to (3, 4) and to (5, 12). Which point is farther?

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Question 11

Find the distance between A(0, 0) and B(6, 8).

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Question 12

Find the distance between A(2, 3) and B(7, 15).

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Question 13

A circle has centre C(3, 5) and passes through point P(8, 17). Find the radius.

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Question 14

Find the midpoint of A(1, 9) and B(7, 3).

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Question 15

Find the midpoint of A(-5, 8) and B(11, -4).

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Question 16

Find the distance between P(-3, 4) and Q(5, -2).

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Question 17

Two villages A(2, 5) and B(11, 17) are on a map where each unit represents 1 km. Find the straight-line distance between them.

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Question 18

A field is rectangular with corners at (0, 0), (300, 0), (300, 400) and (0, 400) (in metres). Find the diagonal walking distance.

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Question 19

Find the distance from the origin to the point (-9, 12).

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Question 20

A cuboid has dimensions 8 × 5 × 3 cm. Find its volume and surface area.

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Topic 3.1: Volumes and Surface Areas of 3D Shapes Questions

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