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601. A Shuttlecock used for playing has the shape of a frustum of a cone mounted hemisphere. The external diameters of a frustum are 5 cm and 2 cm and the height of the entire shuttle-cock is 7 cm. Find its external surface area.

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602. A solid is in the form of a circular cone mounted on a hemisphere. The radius of the hemisphere Rs. 2.1 cm and the height of the cone is 4cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5cm and its height is 9.8 cm. Find the volume of the water left is the cylinderical tub.

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603. A child rocket toy has a hemispherical base, a cylindrical body and conical box cap the rocket is 20 cm. The hemisphere, the cylinder and the cone has a base diameter of 3cm each and the body of cylinderical box is 8cm long. Find volume of the rocket.

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604. An open metallic bucket is in the shape of a frustum of a cone mounted on hollow cylindrical base made of metallic sheet. If diameters of the circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylinderical portion is 6 cm. Find the area of metallic sheet used to make the bucket. Also, find the volume of water it hold. [Take $straight pi$ = 22/7]

Solution not provided.

Ans. 0.7724 litres

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605.

A conical vessel of radius 6cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the circles, it is just immersed as shown in fig what fraction of water over flows?

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606. A copper wire 4 cm in diameters is evenly wound about a cylinder whose length is 24cm and diameter 20cm. So as to cover the whole surface. Find the length and weight of the wire assuming the specific gravity to be 8.88 gm/cm³.

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607. A lead pencil consist of a cylinder of wood with a solid cylinder of graphite filled into it. The diameter of the pencil is 7 mm, the diameter of the graphite is 7 mm and the length of the pencil is 10 cm. Calculate the weight of the whole pencil, if the specific gravity of the wood is 0.7 gm/cm³ and the graphite is 2.1 gm/cm³.

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608. The cost of putting the total outside surface of a closed cylinderical oil lamp at 60 paise per sq-dm is Rs. 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places.

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609.

From a solid right circular cylinder with height 8cm and radius of the base 6cm, a right circular cone of the same height and the same radius is divided out. Find
(i) the volume of the remaining solid.
(ii) the curved surface area of the cavity formed.

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610. A godown building is in the form as shown in Fig. 13.52. The vertical cross-section parallel to the width side of the building is a rectangle 7 m x 3 m, mounted by a semicircle of radius 3.5 m. The inner measurements of the cuboidal portion of the building are 10 m x 7 m x 3 m. Find the volume of the godown and the totel interior surface area excluding the floor (base).

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