If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of the quadrilateral, find the area of the quadrilateral ABCD.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article.

A heap of rice is in the form of a cone of base diameter 24m and height 3.5 m. Find the volume of the rice. How much is canvas cloth required to just cover the heap?

Find the area of the shaded region in Figure, where arcs are drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square of side 12 cm, [Use π =3.14 ]

The diameters of the lower and upper ends of a bucket in the form of a frustum f a cone are 10 cm and 30 cm respectively. If its height is 24 cm, find:

(i) The area of the metal sheet used to make the bucket.
(ii) Why should we avoid the bucket made by ordinary plastic? [ Use π =3.14 ]

Water is flowing through a cylindrical pipe, of internal diameter 2 cm, into a cylindrical tank of base radius 40 cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour

Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.

A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel.
$\left|\mathrm{Use} \mathrm{\pi }= \frac{22}{7}\right|$

A wooden toy was made by scooping out a hemisphere of same radius fromeach end of a solid cylinder. If the height of the cylinder is 10 cm, and itsbase is of radius 3.5 cm, find the volume of wood in the toy.

$\left|\mathrm{Use} \mathrm{\pi } = \frac{22}{7}\right|$

A bucket open at the top, and made up of a metal sheet is in the form ofa frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively.Find the cost of metal sheet used in it at the rate of Rs 10 per 100 cm2.
$\left(\mathrm{Use} \mathrm{\pi } =3.14\right)$