# CBSE Class 10-Mathematics: Chapter – 13 Surface Areas and Volumes Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 15**:

A solid metallic circular cone height with vertical angle is cut into two parts at the middle point of its height by a plane parallel to the base. If the frustum, so obtained be drawn into a wire of diameter . Find the length of the wire.

**Answer**:

Let be the two ends of the frustum

Volume of frustum

Since the frustum is drawn into a wire of length

Volume of frustum volume of cylinder

**Question 16**:

The lower portion of a haystack is an inverted cone frustum and the upper part is a cone find the total volume of the haystack.

**Answer**:

**Question 17**:

A vessel in shape of an inverted cone is surmounted by a cylinder has a common radius of this was filled with liquid till it covered one third the height of the cylinder. If the height of each part is and the vessel is turned upside down. Find the volume of the liquid and to what height will it reach in the cylindrical part.

**Answer**:

Volume of liquid in the vessel

Height of cylindrical part

## 1 Mark Questions

**Question 1**:

A metallic sphere of radius is meted and then recast into small cones each of radius and height , the number of such cones is

(a)

(b)

(c)

(d)

**Answer**:

(b)

**Question 2**:

A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, the radius of the base of the cone is

(a)

(b)

(c)

(d)

**Answer**:

(a)

**Question 3**:

During conversion of a solid from one shape to another, the volume of new shape will

(a) Increase

(b) Decrease

(c) Remain unaltered

(d) Be doubled

**Answer**:

(c) Remain unaltered

**Question 4**:

A right circular cylinder of radius and height (h > 2r) just encloses a sphere of diameter

(a)

(b)

(c)

(d)

**Answer**:

(b)