NCERT Class 10 Maths — Chapter 12

Exercise 12.3: Conversion of Solids

When a solid is melted and recast into another shape, the volume stays the same. Find dimensions of the new shape.

recastingmelting and reshapingvolume conservation

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Extra Practice Questions

These questions cover the same concepts as Exercise 12.3. Try solving them to build confidence before or after the textbook exercise.

A solid metallic sphere of radius 3 cm is melted and recast into a solid cylinder of radius 1 cm. What is the height of the cylinder?

A.A) 9 cm

B.B) 18 cm

C.C) 27 cm

D.D) 36 cm

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 6 cm and the diameter of the base is 4 cm. What is the volume of the toy? (Use π = 22/7)

A.25.14 cm³

B.33.52 cm³

C.41.90 cm³

D.50.28 cm³

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. If the radius of the cylinder is 60 cm and its height is 180 cm, find the volume of water left in the cylinder. (Use π = 22/7)

A.102432 cm³

B.108432 cm³

C.110880 cm³

D.113142.86 cm³

A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around it to a width of 5 m to form an embankment. What is the height of the embankment?

A.A) 4.67 m

B.B) 7 m

C.C) 9.33 m

D.D) 18.67 m

A container, open from the top and made of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the metal sheet used to make the container, if it costs ₹8 per 100 cm². (Use π = 3.14)

A.₹145.42

B.₹157.00

C.₹168.96

D.₹156.77

Water flows through a cylindrical pipe of internal diameter 14 cm at the rate of 20 km/hour into a rectangular tank 50 m long and 44 m wide. In how much time will the water level rise by 7 cm in the tank?

A.15 minutes

B.30 minutes

C.45 minutes

D.60 minutes

A metallic container, open at the top, is in the shape of a frustum of a cone with a height of 16 cm and radii of its lower and upper circular ends as 8 cm and 20 cm respectively. To find the area of the metal sheet used to make this container, what surfaces must be considered?

A.A) Curved Surface Area of frustum only.

B.B) Curved Surface Area of frustum + Area of upper circular end.

C.C) Curved Surface Area of frustum + Area of lower circular end.

D.D) Curved Surface Area of frustum + Area of both circular ends.

A water storage tank is designed in the shape of a frustum of a cone. If R and r are the radii of its top and bottom circular bases respectively, and h is its vertical height, which of the following expressions correctly represents the volume of water it can hold?

A.A) (1/3)πh(R² + r²)

B.B) (1/3)πh(R² + r² + Rr)

C.C) (1/3)πh(R - r)²

D.D) πh(R² + r² + Rr)

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the conical part is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas at the rate of ₹500 per m². (Use π = 22/7)

A.57.2 m², ₹28600

B.44 m², ₹22000

C.50.28 m², ₹25140

D.38.4 m², ₹19200

An engineering student, Rachit, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its total length is 12 cm. If each cone has a height of 2 cm, find the total volume of air contained in the model. (Use π = 22/7)

A.55.44 cm³

B.66.00 cm³

C.72.27 cm³

D.79.20 cm³

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