Plane and Solid Geometry

The side of a square is x meters , The midpoints of Its

sides are Joined to form another square whose area

Is 16 m². Find the value of x.

• 0.707 m

• 2.83 m

• 4.24 m

• 5.66 m

A circle which has an area of 144pi cm² Is cut Into

two segments by a chord that Is 6 cm from the

center of the circle. What Is area of the smaller

segment?

• 18.85 cm²

• 9 cm²

• 254.47 cm²

• 88.45 cm²

A cube has an edge equal to 5cm The length of the

diagonal of a cube is

• 5 cm

• 7.07 cm

• 8.66 cm

• 10 cm

A cube has an edge equal to the diagonal of another

cube. Find the ratio of their volumes

• 5.20

• 1.73

• 0.577

• 0.33

The bases of a triangular right prism are 12 cm apart.

Find the volume if one side of the equilateral triangle

base measures 6 cm.

• 15.59 cm³

• 187.08 cm³

• 247.18 cm³

• 216 cm³

The lateral area of a right cylindrlcal tank is 48π m²

and its volume is 72π m³. Find the altitude of the

tank.

• 8 m

• 3 m

• 72 m

• 24 m

A closed cylindrical tank 10 ft In height and 4 ft in

diameter contains water with a depth of 3 ft and 5

in. What would be the height of the water when the

tank Is lying in a horizonal position.

• 0.5 ft

• 1.5 ft

• 4.29 ft

• 3.42 ft

An Inverted square pyramid has a height equal to 8

m and a top edge equal to 3 m. It contains water to a

depth of 5 m. What is the volume of the water In the

to tank?

• 24 m³

• 18.14 m³

• 5.86 m³

• 4 m³

Find the ratio of the diagonals of a rhombus whose

side is 3 m and the angle opposite the shorter

diagonal is 45°,

• 2.296

• 5.543

• 0.414

• 0.314

Find the area of the rhombus whose diagonals are and 2.296 m and 5.543 m.

• 6.36 m²

• 12.73 m²

• 0.414 m²

• 0.314 m²