Proofs of angles sum of a triangle = 180 degrees

The sum of angles on a straight line is 180^o.

EVALUATION

1. Three angles of a triangle x, 2x and 3x. find the value of x and hence find the angles.
2. The ratio of the angles of a triangle is 2, 3 and 4. Find the angles.

GENERAL EVALUATION

1. A lampshade in the form of a frustum of a cone has a height of 12cm and an upper and lower diameters of 10cm and 20cm.

a. what is the curved surface area of the frustum?

b. What is the volume of the frustum? 

c.  Give both answers in terms of π

2.Afrustum of a pyramid is 16cm square at the bottom, 6cm square at the top and 12 cm high.  Find the volume of the frustum.

READING ASSIGNMENT

NGM SS Bk 1 pages 173-175 Ex 15c Nos 6 and 9 pg 175.

WEEKEND ASSIGNMENT

1. Calculate the volume in cm³ of the material in a cylindrical pipe 1.8m long, the internal and external diameters being 16cm and 18 respectively.

1. A storage container is in the form of a  frustum of a right pyramid 4m square at the top and 2.5m square at the bottom.  If the container is 3m deep. What is its capacity in m³?
2. Three angles of a triangle are (5x – 7)^o, (2x + 15)^o and (2x + 1)^o. find the value of x and hence find the largest and the smallest angles.

THEORY

1. A right pyramid on a base 10m square is 15m high.

(a) Find the volume of the pyramid.

(b) If the top 6m of the pyramid are removed, what is the volume of the remaining frustum?

2. The cone in the figure below is exactly half full of water by volume.  How deep is the water in the cone?