Long Answer Type
Short Answer TypeVolume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?
The 3/4th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in a cylindrical vessel.
In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
Long Answer TypeIn a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of the hospital whose length is 25 m and breadth is 20 m. If the tank is filled completely then what will be the height of standing water used for irrigating the park. Write your views on recycling of water.
Diameter of cylinder (d) = 2 m
Radius of cylinder (r) = 1 m
Height of cylinder (H) = 5 m
Volume of cylindrical tank, Vc = πr2H = π×(1)2×5=5π m
Length of the park (l) = 25 m
Breadth of park (b) = 20 m
the height of standing water in the park = h
Volume of water in the park = lbh = 25×20×h
Now water from the tank is used to irrigate the park. So,
Volume of cylindrical tank = Volume of water in the park
⇒5π=25×20×h
⇒5π/25×20=h
⇒h=π/100 m
⇒h=0.0314 m
Through recycling of water, better use of the natural resource occurs without wastage. It helps in reducing and preventing pollution.
It thus helps in conserving water. This keeps the greenery alive in urban areas like in parks gardens etc.
In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.
The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.
Short Answer TypeIf A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.
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