NCERT Class 10 Chapter 10 Surface Areas and Volumes Official CBSE Board Sample Problems Short Answer

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Question

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14cm and the total height of the vessel is 13cm. Find the inner surface area of the vessel.

Solution

Ans. Diameter of the hollow hemisphere= 14 cm

Radius of the hollow hemisphere;

Total height of the vessel =13 cm

Height of the hollow cylinder

Inner surface area of the vessel

Inner surface area of the hollow hemisphere + Inner surface area of the hollow cylinder

Diameter of the hollow hemisphere

Diameter of the Hollow Hemisphere

Diameter of the hollow hemisphere

Question

A fez, the cap used by the Turks, is shaped like the frustum of a cone (see figure). If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

Solution

The cap used by the Turks

The Cap Used by the Turks

The cap used by the Turks

Ans. Here,

Surface area

Question

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of i two circular ends are 4cm and 2cm. Find the capacity of the glass.

Solution

Ans. Abbreviation: CSA=Curved Surface Area

TSA =Total Surface Area

V=Volume

Here,

:. Capacityofthe g1ass

Shape of a frustum

Shape of a Frustum

Shape of a frustum

Question

A 20 m deep well with diameter 7m is dug and the earth from digging is evenly spread out to form a platform 22m by 14 m. find the height of the platform.

Solution

Ans. Diameter of well =7 m

Radius of well (r)

Arid Depth of earth dug (h) =20 m

Length of platform (l) = 22m, Breadth of platform (b) = 14m

Let height of the platform be h’ m

According to question,

Volume of earth dug Volume of platform

Question

Metallic spheres of radii 6 cm, 8cm and 10 cm respectively are meIted to form a single solid sphere. Find the radius of the resulting sphere.

Solution

Ans4 let the volume of resulting sphere he r cm.

According to question

Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15cm by 10cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth id 1.4 cm. find the volume of wood in the entire stand (see figure).

Solution

Ans. Volume of the cuboid

Volume of conical depression

Volume of four conical depressions

Volume of the wood in the entire stand

Question

In figure, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of rupees 500/sq. metre. (Use)

A tent is in the shape of a cylinder

A Tent is in the Shape of a Cylinder

A tent is in the shape of a cylinder

Solution

Area canvas needed = curved surface area of cylinder + curved surface area of cone

Cost of canvas

Question

A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy (use )

Solution

Hemisphere of base diameter

Hemisphere of Base Diameter

Hemisphere of base diameter

Here, given that

Also, slant height of cone,

Curved Surface Area of cone

Surface area of hemisphere

Hence, Total Surface Area of toy = Surface area of hemisphere + Curved Surface Area of cone

Question

The sum of the radius of base and height of a solid right circular cylinder is 37 cm.

If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder, (use)

Solution

The sum of the radius

The Sum of the Radius

The sum of the radius

Here [Given, where radius, height]

Total surface area of cylinder

Given,

Hence, volume of cylinder

Question

A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around ¡tin the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment?

Solution

Radius of the well = 2m, height of the well = 21 m

Volume of the earth dug out

=

Radius of embankment = Radius of well + width of embankment

Volume of embankment

As per condition,

Volume of earth dug out = Volume of embankment

Height of embankment,

Question

A sphere of diameter 6 cm is dropped into a right circular cylindrical vessel, partly filled with water. The diameter of the cylindrical vessel is 12cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

Solution

Volume of water in the cylinder displaced by the sphere = volume of sphere.

h = 1 cm

Water level will rise by 1 cm.

Question

From a solid cylinder whose height is 12cm and diameter 10cm, a conical cavity with the same base and height is taken out. Find the total surface area of the remaining solid.

Solution

Total surface area of the resulting solid =

Question

Three identical cubes each of volume 343 are joined end to end. Find the surface area of the resulting cuboid.

Solution

Vol of a cube =

Sides of cuboid are 1=21 cm, b=7cm and h =7cm

Question

A solid metallic sphere of diameter 16 cm is melted and recast into a number of smaller cones, each of radius 4cm and height 8cm. Find the number of cones thus formed.

Solution

Volume of metal sphere =

Volume of one small cone =

Number of cones =

=16

Question

From a solid cylinder of height 24cm and radius 7cm, a conical cavity of the same height and same radius is taken out. Find the volume of remaining solid.

Solution

For Karuna

Volume of lce cream

For Rajat

Volume of ice cream=

Volume for Rajat’s Ice-cream> Volume for Karunas Ice cream

Rajat’s deal is better.

Question

Karuna and Rajat went to an ice cream parlor and purchased same flavour ice creams. Karuna bought ice cream (in a plastic cone of radius 3.5 cm and height 7 cm) for Rs. 20. Rajat bought ice cream (in a plastic cylinder for radius and height 7 cm and 3.5 cm) for Rs. 20. Which is a better deal? Why?

Solution

For Karuna

Volume of lce cream

For Rajat

Volume of ice cream=

Volume for Rajat’s Ice-cream> Volume for Karunas Ice cream

Rajat’s deal is better.

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