Circles, Area, Surface Area and Volume: math test, Grade 7 – download the PDF

1 A circle / 3 pts

A circle has a diameter of 20 cm. Use \(\pi \approx 3.14\).

1. What is its radius?
2. Find its circumference.
3. Find its area.

2 Triangles and quadrilaterals / 3 pts

Find the area of each shape.

1. A triangle with a base of 15 cm and a height of 8 cm.
2. A parallelogram with a base of 12 cm and a height of 7.5 cm.
3. A trapezoid with parallel sides of 11 cm and 17 cm and a height of 6 cm.

3 A composite figure / 4 pts

A banner is a rectangle 12 in wide and 8 in tall, with an isosceles triangle on top. The triangle has a base of 12 in (the top side of the rectangle) and a height of 5 in.

1. Find the area of the rectangle.
2. Find the area of the triangle.
3. Find the area of the whole banner. Write a sentence.

4 A triangular prism / 4 pts

The bases of a right prism are right triangles with legs of 5 cm and 12 cm and a hypotenuse of 13 cm. The prism is 10 cm long.

1. Find its volume.
2. Find its surface area.

5 A square pyramid / 3 pts

A square pyramid has a base side of 12 m. The slant height of each triangular face is 10 m. Find its surface area.

6 A fish tank / 3 pts

A rectangular fish tank is 50 cm long, 30 cm wide and 40 cm tall. (\(1 \text{ L} = 1{,}000 \text{ cm}^3\))

1. Find the volume of the tank.
2. The water is 30 cm deep. Find the volume of the water.
3. How many liters of water is that?