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Surface Areas and Volumes

Long Answer Type

711. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).

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712. From each end of a solid metal cylinder, metal was scooped out in the hemispherical form of the same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire. ( π = 22/7)

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Short Answer Type

713.

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

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714.

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.

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715.
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.

Since OACB is a quadrant, it will subtend 90° angles at O.
Area of quadrant OACB
$space equals space 90 to the power of straight o over 360 to the power of straight o straight x space πr squared space equals space 1 fourth space straight x 22 over 7 space straight x space left parenthesis 3.5 right parenthesis squared space equals space 1 fourth space straight x 22 over 7 space straight x open parentheses 7 over 2 space close parentheses squared space equals space fraction numerator 11 space straight x 7 space straight x 7 over denominator 2 space straight x 7 space straight x space 2 space straight x space 2 end fraction space equals space 77 over 8 space cm squared$

Area of ΔOBD
$space equals space fraction numerator 1 over denominator space 2 end fraction space straight x space OB space straight x space OD equals 1 half space straight x 3.5 space straight x space 2 space equals space 1 half space straight x 7 over 2 space straight x space 2 space equals space 7 over 2 space cm squared$
Area of the shaded region
= Area of quadrant OACB − Area of ΔOBD
$77 over 8 minus 7 over 2 space equals space fraction numerator 77 minus 28 over denominator 8 end fraction space equals space 49 over 8 space cm squared$

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Long Answer Type

716.

In 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.

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717.

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.

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718.

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.

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