$CATEGORY: Maths - TicTacLearn/12. Surface areas and volumes/12. Surface areas and volumes--Volume of a Combination of Solids

//Multiple Choice

What does the volume of an object represent? {
~ The surface area of the object
= The space enclosed by the object
~ The weight of the object
~ The fluid it can hold
}

The formula for the volume of a cylinder is ____. {
= πr²h
~ 1/3 πr²h
~ 4/3 πr³
~ 2πrh
}

What is the relationship between the radius of a sphere and its volume? {
~ Volume is directly proportional to radius
~ Volume is proportional to the square of radius
= Volume is proportional to the cube of radius
~ Volume does not depend on radius
}

To find the volume of a solid formed by combining two shapes, we ____. {
~ Multiply their volumes
= Add their volumes
~ Subtract the smaller volume from the larger one
~ Divide their volumes
}

In the example of the pencil (Video 1), what three shapes combine to form it? {
~ Cone, sphere, and cuboid
= Hemisphere, cylinder, and cone
~ Cylinder, sphere, and cone
~ Hemisphere, cone, and cuboid
}

What happens to the volume of a cone when its height is halved, keeping the radius constant? {
~ It doubles
= It becomes half
~ It remains the same
~ It becomes one-fourth
}

In the wooden block example (Video 1), what operation is used to find the remaining volume? {
~ Addition of volumes
= Subtraction of volumes
~ Multiplication of dimensions
~ Division of dimensions
}

Which solid's volume is calculated using 4/3 πr³? {
= Sphere
~ Cylinder
~ Cone
~ Cuboid
}

What is the volume of a hemisphere with radius r? {
= 2/3 πr³
~ πr³
~ 4/3 πr³
~ 2πr³
}

When one solid is subtracted from another, the resulting volume is? {
~ A sum of their dimensions
~ The volume of the smaller solid
= The volume of the remaining part
~ Zero
}

//True or False

Volume and capacity are the same concepts. {F}

The formula for the volume of a sphere is 4/3 πr³. {T}

To calculate the volume of a combination of solids, we multiply their volumes. {F}

A hemisphere has half the volume of a sphere with the same radius. {T}

The volume of water displaced by an object equals its weight. {F}

//Numericals

Find the volume of a cone with radius 3 cm and height 8 cm. {
~ 24π cubic cm
~ 72π cubic cm
~ 24 cubic cm
~ 24π/3 cubic cm
}

A cuboid has dimensions 10 cm × 5 cm × 8 cm. Find its volume. {
~ 500 cubic cm
= 400 cubic cm
~ 600 cubic cm
~ 800 cubic cm
}

Calculate the total volume of a solid formed by a cylinder (radius \=2 cm, height \= 5 cm) and a hemisphere (radius \= 2 cm). {
~ 25.13 cubic cm
= 41.89 cubic cm
~ 36.17 cubic cm
~ 50.27 cubic cm
}

In the pencil example, verify the total volume when combining a cone, cylinder, and hemisphere. {
~ 45.24 cubic cm
= 49.24 cubic cm
~ 52.18 cubic cm
~ 56.52 cubic cm
}

Find the remaining volume of water when a ball (radius \= 3 cm) is immersed in a conical vessel (radius \= 6 cm, height \= 8 cm). {
= 188.57 cubic cm
~ 170.23 cubic cm
~ 192.41 cubic cm
~ 165.89 cubic cm
}

//Fill in the blanks

The space enclosed by an object is called its ____. {
~ Capacity
= Volume
~ Surface Area
~ Height
}

The capacity of an object is the volume of ____ that it can hold. {
~ Gas
= Fluid
~ Solid
~ Surface
}

The volume of a cone is ____ the volume of a cylinder with the same base and height. {
~ Half
= One-third
~ Two-thirds
~ Equal to
}

When two solids are combined, their total volume is the ____ of their individual volumes. {
~ Product
= Sum
~ Difference
~ Ratio
}

If the radius of a sphere doubles, its volume increases by a factor of ____. {
~ 2
~ 4
~ 6
= 8
}

The radius of a hemisphere is 4 cm. Its volume is ____. {
= 256/3 π cm³
~ 64π cm³
~ 512/3 π cm³
~ 128π cm³
}

The volume of water left in a conical vessel after a sphere is immersed equals the volume of the cone ____ the volume of the sphere. {
~ Plus
= Minus
~ Divided by
~ Multiplied by
}

The height of a cone is 12 cm, and the radius is 4 cm. The volume of the cone is ____. {
= 64π cm³
~ 64/3 π cm³
~ 192/3 π cm³
~ 192π cm³
}

A combination of a cone and a hemisphere forms a solid. The total volume of the solid is the ____ of the cone and hemisphere volumes. {
~ Product
= Sum
~ Difference
~ Ratio
}

In the wooden block example (Video 1), the radius of the cone removed is 2 cm, and its height is 10 cm. The volume of the removed cone is ____. {
= 40/3 π cm³
~ 40π cm³
~ 80/3 π cm³
~ 20/3 π cm³
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
=Volume of a removed solid -> Subtract smaller volume from larger volume
=Radius of a sphere -> Pythagoras theorem or geometry
=Combined volume calculation -> Add volumes of individual solids
=Capacity of an object -> Space for holding fluid
=Volume of displaced water -> Equal to the volume of the submerged object
}



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