Surface Areas and Volumes: Class 10 Maths Practice Questions

Riya, a craft teacher at a government school in Jaipur, prepared a decorative model for the annual science exhibition by joining a solid cone mounted on top of a solid hemisphere, both having the same base radius of 7 cm. The height of the cone is 24 cm and the radius of the hemisphere is also 7 cm. The model is to be painted and displayed as a showpiece representing a traditional lamp design.

Riya, a craft teacher at a government school in Jaipur, prepared a decorative model for the annual science exhibition by joining a solid cone mounted on top of a solid hemisphere, both having the same base radius of 7 cm. The height of the cone is 24 cm and the radius of the hemisphere is also 7 cm. The model is to be painted and displayed as a showpiece representing a traditional lamp design.

A school is organising a Science Fair. Students in the craft club decide to make decorative items using solid clay. Priya takes a solid clay cylinder of radius 6 cm and height 12 cm. She reshapes the entire clay into small solid spheres, each of radius 1 cm, without any wastage.

A school is organising a Science Fair. Students in the craft club decide to make decorative items using solid clay. Priya takes a solid clay cylinder of radius 6 cm and height 12 cm. She reshapes the entire clay into small solid spheres, each of radius 1 cm, without any wastage.

(i) What is the volume of the original solid clay cylinder? [1 mark]
(ii) What is the volume of each small solid sphere? [1 mark]
(iii) How many complete small solid spheres can Priya make from the clay? [2 marks]

A school is organising a Science Fair and students are making decorative pieces. Riya decides to make a pencil-shaped showpiece by joining a cylinder and a cone. The cylinder has radius 1.4 cm and height 10 cm. The cone is placed on top of the cylinder and has the same base radius as the cylinder and a height of 3 cm. (Take π = 22/7)

A school is organising a Science Fair and students are making decorative pieces. Riya decides to make a pencil-shaped showpiece by joining a cylinder and a cone. The cylinder has radius 1.4 cm and height 10 cm. The cone is placed on top of the cylinder and has the same base radius as the cylinder and a height of 3 cm.

(i) Find the volume of the cylindrical part of the showpiece.
(ii) Find the volume of the conical part of the showpiece.
(iii) Find the total volume of the showpiece. OR Find how much cardboard (curved surface area) is needed to cover only the lateral surface of the cylinder and the slant surface of the cone. (Take π = 22/7)

A decorative pen stand is made by joining a hollow cylinder (open at both ends) with a hollow cone fixed at its bottom. The cylindrical part has height 10 cm and radius 3.5 cm. The conical part has height 4 cm and the same base radius of 3.5 cm. The outer surface, including the base circle of the cone, is to be painted.

A decorative pen stand is made by joining a hollow cylinder open at both ends with a hollow cone fixed at its bottom (closed), as shown in the figure. The pen stand is to be gifted after painting its entire outer surface (including the base of the cone).

The dimensions are:
• Cylindrical part: height = 10 cm, radius = 3.5 cm
• Conical part: height = 4 cm, radius = 3.5 cm (same as cylinder)

Based on this, answer the following:
(i) What is the slant height of the conical part? [1 mark]
(ii) What is the curved surface area of the cylindrical part? [1 mark]
(iii) Find the total surface area to be painted (curved surface of cylinder + curved surface of cone + base of cone). [2 marks]

(Use π = 22/7)

A school is organising a Science Fair. Priya makes a Rocket Model by placing a solid cone on top of a solid cylinder. The cylinder has height 21 cm and radius 7 cm. The cone has the same base radius 7 cm and height 9 cm. The model is to be painted on all outer surfaces except the bottom circular base. [Use π = 22/7]

A school is organising a Science Fair and students are asked to make models using everyday objects. Priya decides to make a 'Rocket Model' by placing a cone on top of a cylinder. She uses a solid wooden cylinder of height 21 cm and radius 7 cm. On top of the cylinder, she fixes a solid cone of the same base radius (7 cm) and height 9 cm. The entire outer surface of the model (except the bottom circular base) is to be painted.

(i) What is the slant height of the cone fixed on top? (1 mark)
(ii) What is the curved surface area of the cylindrical part that is to be painted? (1 mark)
(iii) Find the total surface area of the rocket model that is to be painted (excluding the bottom base). (2 marks)

[Use π = 22/7]

A school's science club makes paperweights by fixing a solid hemisphere on top of a solid cylinder. Both shapes share the same radius of 3.5 cm. The height of the cylinder is 5 cm. Use π = 22/7.

A school's science club is making decorative paperweights to sell at the annual fair. Each paperweight is made by placing a solid hemisphere exactly on top of a solid cylinder, both having the same radius of 3.5 cm. The height of the cylinder is 5 cm.

(i) What is the curved surface area of the hemisphere? [1 mark]
(ii) What is the total surface area of the cylindrical part (excluding the top face, since the hemisphere sits on it)? [1 mark]
(iii) Find the total surface area of the combined solid (paperweight). [2 marks]

A decorative table lamp shade is made by combining a hollow cone and a hollow cylinder, both open at their ends. The conical top has a slant height of 10 cm and base radius of 6 cm. The cylindrical base has the same radius (6 cm) and height of 8 cm. A craftsman wants to cover the entire outer curved surface of the shade with metallic foil costing ₹15 per 100 cm². He also melts a solid sphere of radius 6 cm to cast solid cylindrical rods of radius 1 cm and height 4 cm.

A decorative table lamp shade is made by combining a hollow cone and a hollow cylinder, both open at their ends, as shown in the description below. The conical top has a slant height of 10 cm and base radius of 6 cm. The cylindrical base has the same radius as the cone (6 cm) and a height of 8 cm. A craftsman wants to cover the entire outer surface (curved surfaces only) of the shade with a special metallic foil that costs ₹15 per 100 cm². Additionally, the craftsman melts a solid sphere of radius 6 cm to cast solid cylindrical rods of radius 1 cm and height 4 cm to be used as lamp stand supports.

Based on the above information, answer the following questions:
(i) Find the curved surface area of the conical part of the shade. [1 mark]
(ii) Find the total curved surface area of the lamp shade (cone + cylinder) that needs to be covered with foil. [1 mark]
(iii) Find the total cost of covering the shade with metallic foil. [2 marks]
OR
(iii) Find the number of solid cylindrical rods that can be cast from the melted solid sphere of radius 6 cm. [2 marks]

A school craft club is making decorative paperweights to sell at the annual fair. Each paperweight is made by placing a solid metallic cone on top of a solid metallic cylinder, both sharing the same base radius of 7 cm. The height of the cylinder is 15 cm and the slant height of the cone is 25 cm.

A school craft club is making decorative paperweights to sell at the annual fair. Each paperweight is made by placing a solid metallic cone on top of a solid metallic cylinder, both sharing the same base radius of 7 cm. The height of the cylinder is 15 cm and the slant height of the cone is 25 cm.

(i) Find the height of the cone.
(ii) Find the curved surface area of the cone.
(iii) Find the total surface area of the paperweight (the circular base of the cylinder is the bottom of the paperweight, and the cone sits exactly on top of the cylinder, so the top circular face of the cylinder is not exposed).

OR

(iii) If 20 such paperweights are to be painted, and the cost of painting is ₹5 per cm², find the total cost of painting all 20 paperweights. (Use π = 22/7)

A solid cylinder of radius r and height h is melted and recast into a solid hemisphere of the same radius r. The ratio of the curved surface area of the cylinder (excluding the two circular ends) to the curved surface area of the hemisphere is:

The curved surface area of a cone is 550 cm² and its slant height is 25 cm. What is the radius of the base of the cone? (Take π = 22/7)

A decorative cap is in the shape of a cone with slant height 25 cm and base radius 10 cm. What is the curved surface area of the cap? (Take π = 22/7)

A solid sphere of radius 6 cm is cut into two equal hemispheres. The ratio of the curved surface area of the sphere to the sum of the curved surface areas of the two hemispheres taken together is:

The total surface area of a solid hemisphere is 675π cm². What is the radius of the hemisphere?

A decorative cap is in the shape of a cone with slant height 25 cm and base radius 7 cm. What is the curved surface area of the cap? (Take π = 22/7)

The curved surface area of a cylinder of height 14 cm is 528 cm². What is the radius of the cylinder? (Take π = 22/7)

The ratio of the total surface area of a solid cone (excluding the base) to the product of its slant height and base radius is:

The curved surface area of a cone having height 40 cm and base radius 9 cm is (Take π = 22/7):

A cone has a base diameter of 28 cm and a perpendicular height of 48 cm. What is the curved surface area of the cone? (Take π = 22/7)

A heap of grain is in the form of a cone of diameter 18 m and height 12 m. What is the curved surface area of the cone that represents the heap?

A solid sphere of radius r is cut into two equal hemispheres. The ratio of the curved surface area of the sphere to the total surface area of one hemisphere is:

The curved surface area of a cone of slant height 13 cm is 204.1 cm². What is the radius of the base of the cone? (Take π = 3.14)

A conical tent has a vertical height of 8 m and a base radius of 6 m. What is the curved surface area of the tent? (Take π = 3.14)

The ratio of the curved surface area of a solid sphere to the square of its radius is:

The curved surface area of a cylinder of radius 4 cm is 176 cm². What is the height of the cylinder? (Take π = 22/7)

A solid cylinder is melted and recast into a solid cone of the same base radius. If the height of the cylinder is 9 cm, what is the height of the cone formed?

The curved surface area of a cylinder of radius 3 cm is 132 cm². What is the height of the cylinder? (Take π = 22/7)

The curved surface area of a cylinder of radius 7 cm is 308 cm². What is the height of the cylinder? (Take π = 22/7)

The ratio of the total surface area of a solid hemisphere to the curved surface area of a sphere of the same radius is:

A solid toy is in the shape of a hemisphere of radius 4 cm placed on top of a cylinder of the same base radius and height 6 cm. The total surface area of the combined solid is:

A solid metallic hemisphere of base radius 9 cm is melted and recast into small solid cylinders, each of base radius 1 cm and height $\frac{3}{2}$ cm. Find the number of cylinders so formed. (Use $\pi =\frac{22}{7}$)