Surface Area and Volume Word problems

**Page 1**

1.

An adhesive compound in liquid form is prepared in a container of hemispherical shape having a radius of 180 cm. This compound is to be packed in cylindrical bottles of radius 1 cm and height of 4 cm. How many bottles are needed if the liquid prepared exactly fills the container? [Take $\pi $ = 3.]

a. | 1.94 | ||

b. | 388800 | ||

c. | 972000 | ||

d. | 16200 |

[Formula.]

Volume of the liquid = Volume of the hemisphere

[Volume of the hemisphere =

Volume of one bottle

[Volume of the cylinder =

Number of bottles

[From steps 2 and 3.]

Correct answer : (3)

2.

Find the surface area of the earth assuming the earth to be a sphere of radius 6369 km.

a. | 509485853 square km | ||

b. | 509485862 square.km | ||

c. | 509485863 square km | ||

d. | 509485861 square km |

[Given.]

The surface area of the earth = 4

[Formula.]

= 4

[Substitute the value of

= 509485862 square km

[Simplify.]

Correct answer : (2)

3.

$\frac{3}{4}$ of the earth's surface area is covered with water. Find the surface area of the land if the earth can be assumed as a sphere of radius 6366 km.

a. | 6366 square km | ||

b. | 127251501 square km | ||

c. | 4774 square km | ||

d. | 19098 square km |

[Given.]

The surface area of the earth = 4

[Formula.]

= 4

= 509006007

The surface area which is covered with water =

The surface area of the land on earth = (1-

=

=

= 127251501 square km

Correct answer : (2)

4.

$\frac{3}{4}$ of the earth's surface area is covered with water. Find the surface area covered by water if the earth can be assumed as a sphere of radius 6365 km.

a. | 127211526.50 square.km | ||

b. | 381634579.50 square.km | ||

c. | 190817289.75 square.km | ||

d. | 63605763.25 square.km |

[Given.]

The surface area of the earth = 4

[Formula.]

= 4

= 508846106 square.km

The surface area which is covered with water =

=

= 381634579.50 sq.km

Correct answer : (2)

5.

Find the maximum volume of the sphere in cubic cm that can be carved out of a cube of side 20 cm. [Take $\pi $ = 3.14]

a. | 4186.66 cm ^{3} | ||

b. | 33493.3 cm ^{3} | ||

c. | 8000 cm ^{3} | ||

d. | 1256.8 cm ^{3} |

[Given.]

The maximum radius of sphere that can be carved out of the cube =

The maximum volume of the sphere that can be carved out of the cube =

[Formula.]

=

= 4186.66 cm

Correct answer : (1)

6.

Find the sum of the volume of a cone with radius 1 cm and height 5 cm and the volume of a sphere of radius 1 cm. [Take $\pi $ = 3.]

a. | 9 cm³ | ||

b. | 14 cm³ | ||

c. | 13 cm³ | ||

d. | 12 cm³ |

[Volume of the cone =

Volume of the sphere =

[Volume of a sphere =

Sum of the volumes = 5 + 4 = 9 cm

[Simplify.]

Correct answer : (1)

7.

A cylindrical jar of radius 15 cm is filled with water upto a height of 25 cm. 15 spherical balls of radii 2 cm each are immersed in the jar. Find the new level to which water is filled in the jar. [Take $\pi $ = 3.]

a. | 25.71 cm | ||

b. | 32.71 cm | ||

c. | 27.71 cm | ||

d. | 30.71 cm |

[Volume of the sphere =

Volume of 15 spheres = 15 × 32 = 480 cm

[Multiply.]

Volume of water in the jar = 3 × (15

[Volume of the cylinder =

Total volume of water + balls(V)

[Simplify.]

Volume of the water in the cylinder when spherical balls are immersed = 17355 cm

[From step 4.]

[From step 5.]

Height to which water is filled in the jar

Correct answer : (1)

8.

Three hemispheres of radius 1, 2 and 1 respectively are melted to form a sphere. What is the radius of the new sphere formed? [Take $\pi $ = 3.]

a. | $r$ = $\sqrt[3]{15}$ units | ||

b. | $r$ = $\sqrt[3]{3}$ units | ||

c. | $r$ = $\sqrt[3]{10}$ units | ||

d. | $r$ = $\sqrt[3]{5}$ units |

[Formula]

Volumes of three hemispheres =

=

As the sphere is formed by melting three hemispheres, volume of the sphere is equal to the volumes of three hemispheres.

Correct answer : (4)

9.

A water tank is in the form of a hemisphere with radius 5 m. It is filled with water at a rate of 8 litres/sec. How much time will it take to fill the tank?

[Given.]

Volume of the tank =

[Volume of the tank =

[1 m

Rate of filling the water = 8 litres/sec,

[Given.]

Time taken to fill the tank =

[Formula.]

Time taken to fill the tank =

= 31250 seconds = 520.83 min

[Simplify.]

[1 minute = 60 seconds.]

Correct answer : (0)

10.

A rectangular block of lead with dimension 43 cm × 53 cm × 63 cm is melted to mould spherical balls of 3 cm radius. How many balls are made?

(Round your answer to nearest whole number and take $\pi $ = 3. ]

(Round your answer to nearest whole number and take $\pi $ = 3. ]

a. | 1829 | ||

b. | 1629 | ||

c. | 1429 | ||

d. | 1329 |

[Formula.]

Total volume of lead = 43 cm × 53 cm × 63 cm

[Given.]

Volume of one spherical ball =

[Volume of a sphere =

Number of spherical balls =

[Simplify.]

Correct answer : (4)