The diameter of a circular pond is 100 meter and a pillar is fixed at the centre of the pond. A person finds the angle of elevation of the top of the pillar is 0° from the bank of the pond. If the depth of the pond is 1.5 meter and total height of the pillar is 51.5 meter, then find the value of theta.​

Step-by-step explanation:

This shows us that the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying length by breadth for each of them separately and then adding the six areas together.

Now, if we take the length of the cuboid as l, breadth as b and the height as h, then the figure with these dimensions would be like the shape you see in Fig. 13.2(f).

So, the sum of the areas of the six rectangles is:

Area of rectangle 1 (= l × h) + Area of rectangle 2 (= l × b) + Area of rectangle 3 (= l × h ) + Area of rectangle 4 (= l × b) + Area of rectangle 5 (= b × h) + Area of rectangle 6 (= b × h )

= 2(l × b) + 2(b × h) + 2(l × h) = 2(lb + bh + hl)

This gives us:

where l, b and h are respectively the three edges of the cuboid.

Note: The unit of area is taken as the square unit, because we measure the magnitude of a region by filling it with squares of side of unit length.

For example, if we have a cuboid whose length, breadth and height are 15 cm, 10 cm and 20 cm respectively, then its surface area would be:

2[(15 × 10) + (10 × 20) + (20 × 15)] cm2

= 2(150 + 200 + 300) cm2

= 2 × 650 cm2

= 1300 cm2

Recall that a cuboid, whose length, breadth and height are all equal, is called a cube. If each edge of the cube is a, then the surface area of this cube would be 2(a × a + a × a + a × a) i.e., 6a2 (see Fig. 13.3), giving us

where a is the edge of the cube.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

cosine

step-by-step explanation: