8th grade geometry

Question 1

Two triangles are similar. The small one has sides 3 cm and 9 cm. The matching side to 3 cm on the large triangle is 7.5 cm. How long is the side matching 9 cm?

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Question 2

A water bottle is a cylinder 6 cm across and 14 cm tall. How many litres does it hold? (1 litre = 1000 cm³.) Round to 2 decimal places.

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Question 3

Jamal wants to draw a regular polygon with interior angles of 155°. Is that possible?

• A. Yes
• B. No

Question 4

What is each interior angle of a regular pentagon? Round to 1 decimal place if needed.

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Question 5

A right triangle has legs 24 cm and 45 cm. How long is the hypotenuse, in cm?

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Question 6

A triangle has sides 24, 45 and 51. Is it a right triangle?

• A. Yes
• B. No

Question 7

Triangle PQR has P(0, 0), Q(3, 0), R(0, 2). It is translated by (−5, 2). Where does P go?

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Question 8

An ice-cream cone has radius 3 cm and height 6 cm. Find its volume in cm³, to 1 decimal place.

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Question 9

A cone has radius 9 cm and height 3 cm. Its volume is kπ cm³. What is k?

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Question 10

Ava builds a garden frame with sides 8 dm and 15 dm and wants a perfect right-angled corner. How long should the diagonal brace be, in dm?

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Question 11

A cylinder has radius 2 cm and height 10 cm. Find its volume in cm³, to 1 decimal place.

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Question 12

What is each interior angle of a regular polygon with 8 sides, in degrees?

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Question 13

What is the sum of the interior angles of a nonagon (9 sides)?

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Question 14

Rotate (6, −4) 180° about the origin. Type the image like (2, −3).

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Question 15

A cylinder has volume 810π m³ and height 10 m. What is its radius, in m?

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Question 16

In a triangle the two opposite interior angles are (x + 9)° and (2x + 16)°. The exterior angle is 73°. Find x.

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