Volume of Cylindrical Vessel and Juice Glasses Calculation

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Questions and Answers

What is the volume of juice that the cylindrical vessel can hold?

2250π cm³

720π cm³

1440π cm³ (correct)

1800π cm³

How many glasses of juice are sold from the cylindrical vessel?

110

100 (correct)

120

What is the total amount received by the stall keeper when each glass is sold for `15?

`1500 (correct)

`1200

`1650

`1350

What is the circumference of the base of the cylindrical vessel?

132 cm (B) Signup and view all the answers

What is the height of the cylindrical vessel that can hold a certain amount of water?

25 cm (B) Signup and view all the answers

If the lateral surface area of a cylinder is 94.2 cm² and its height is 5 cm, what is the radius of its base?

3 cm (B) Signup and view all the answers

What shape of cone is specifically being discussed in this chapter?

Right circular cone (D) Signup and view all the answers

What does cutting out the paper cone along its side allow you to see?

The slant height l (C) Signup and view all the answers

What is the relationship between the curved portion of Fig. 13.15 (c) and the circular base of the cone?

The curved portion forms the circular base (C) Signup and view all the answers

What shape do the cut portions of the paper resemble?

Triangle (D) Signup and view all the answers

What formula is used to calculate the area of each triangle from the paper cone?

$rac{1}{2} ×$ base of each triangle $×$ height (A) Signup and view all the answers

What does the circumference of the base of a cone represent?

Perimeter of the base (C) Signup and view all the answers

In a village with a population of 4000, each person requires 150 litres of water per day. If the village has a tank measuring 20 m x 15 m x 6 m, for how many days will the water in the tank last?

60 days (B) Signup and view all the answers

A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side length of the new cube?

6 cm (C) Signup and view all the answers

A river is 3 m deep and 40 m wide, flowing at 2 km per hour. How much water, in cubic meters, will fall into the sea in a minute?

800 m³ (D) Signup and view all the answers

If a cuboidal tank has a length of 2.5 m and depth of 10 m, and its capacity is 50000 litres, what is the breadth of the tank?

6 m (A) Signup and view all the answers

A godown measures 40 m x 25 m x 15 m. What is the maximum number of wooden crates, each measuring 1.5 m x 1.25 m x 0.5 m, that can be stored in the godown?

4800 crates (B) Signup and view all the answers

What is the formula to calculate the volume of a cylinder?

$3.14r^2h$ (D) Signup and view all the answers

What is the cost of white-washing the inside of the dome?

` 4989.60 (C) Signup and view all the answers

What is the surface area of one iron sphere if the total surface area S of 27 spheres is melted to form a new sphere?

$4rac{4}{27}S$ (C) Signup and view all the answers

What is the volume of the air inside the dome?

248.48 cubic meters (D) Signup and view all the answers

What is the radius r′ of the new sphere formed by melting 27 solid iron spheres?

$\frac{3r}{2}$ (B) Signup and view all the answers

What is the ratio of the surface area S to the new surface area S′ of the sphere formed by melting 27 solid iron spheres?

$27:1$ (B) Signup and view all the answers

How much medicine (in mm³) is needed to fill a capsule in the shape of a sphere with a diameter of 3.5 mm?

$rac{77}{6}π$ (A) Signup and view all the answers

What is the relationship between the volume of a sphere and the volume of water displaced by it?

They are equal (D) Signup and view all the answers

What conclusion can be drawn from the repeated experiments with spheres of varying radii?

The volume of a sphere is equal to pi times the cube of its radius (D) Signup and view all the answers

What is the formula for finding the volume of a hemisphere?

$\frac{2}{3} \pi r^3$ (B) Signup and view all the answers

What is the volume of a sphere of radius 11.2 cm?

5887.32 cm³ (B) Signup and view all the answers

If a metallic shot-putt is a sphere of radius 4.9 cm, what would be its mass if the density of the metal is 7.8 g per cm³?

201.88 g (B) Signup and view all the answers

What does the formula $V = \frac{4}{3} \pi r^3$ represent in relation to a sphere?

Volume (B) Signup and view all the answers

Study Notes

Cylindrical Vessel

The volume of juice that the cylindrical vessel can hold is unknown.
It can hold an unknown number of glasses of juice, each selling for ₹15.

Cylinder Properties

The circumference of the base of the cylindrical vessel is unknown.
The height of the cylindrical vessel that can hold a certain amount of water is unknown.
If the lateral surface area of a cylinder is 94.2 cm² and its height is 5 cm, the radius of its base is unknown.

Cones

The shape of cone being discussed is a paper cone.
Cutting out the paper cone along its side allows you to see the relationship between the curved portion and the circular base of the cone.
The curved portion of Fig. 13.15 (c) is related to the circular base of the cone.
The cut portions of the paper resemble a rectangle.
The formula to calculate the area of each triangle from the paper cone is unknown.

Circumference and Base of a Cone

The circumference of the base of a cone represents the perimeter of the circular base.

Real-World Applications

In a village with a population of 4000, each person requires 150 litres of water per day.
A tank measuring 20 m x 15 m x 6 m can hold water for an unknown number of days.

Solids

A solid cube of side 12 cm cut into eight cubes of equal volume will have a new cube with a side length of unknown.
A cuboidal tank with a length of 2.5 m, depth of 10 m, and capacity of 50000 litres has a breadth of unknown.
A godown measuring 40 m x 25 m x 15 m can store an unknown number of wooden crates, each measuring 1.5 m x 1.25 m x 0.5 m.

Formulas

The formula to calculate the volume of a cylinder is unknown.

Spheres

The cost of white-washing the inside of the dome is unknown.
The surface area of one iron sphere is related to the total surface area S of 27 spheres melted to form a new sphere.
The volume of the air inside the dome is unknown.
The radius r′ of the new sphere formed by melting 27 solid iron spheres is unknown.
The ratio of the surface area S to the new surface area S′ of the sphere formed by melting 27 solid iron spheres is unknown.
The formula $V = \frac{4}{3} \pi r^3$ represents the volume of a sphere.

Hemisphere and Sphere

The formula for finding the volume of a hemisphere is unknown.
The volume of a sphere of radius 11.2 cm is unknown.
A metallic shot-putt with a radius of 4.9 cm has a mass of unknown if the density of the metal is 7.8 g per cm³.

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Description

Calculate the volume of juice in a cylindrical vessel and the number of glasses a stall keeper can fill with the juice. Practice using formulas for cylinder volume and basic geometry calculations.