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A solid consists of a cone, cylinder and hemisphere joined together as shown in the diagram. Given the dimensions indicated in the diagram, find the volume and surface area of the solid, accurate to $3$ significant figures.

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Grade 6

Volume of cubes and rectangular prisms: word problems

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More problems from Volume of cubes and rectangular prisms: word problems

Question

A cylindrical soda can has a volume of

108\pi\ \text{cm}^{3}

and a height of

12\text{cm}

. What is the surface area of the soda can in square centimeters?

\newline

Choose

1

answer:

\newline

(A)

18\pi\text{cm}^{2}

\newline

(B)

36\pi\text{cm}^{2}

\newline

(C)

72\pi\text{cm}^{2}

\newline

(D)

90\pi\text{cm}^{2}

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Posted 8 months ago

Question

A cake pan is in the shape of a right rectangular prism

20\,\text{cm}

long by

20\,\text{cm}

wide by

5\,\text{cm}

high. The pan contains

1,000\,\text{cm}^3

of batter. Approximately how far is the cake batter from the top of the pan?

\newline

Choose

1

answer:

\newline

(A)

1\,\text{cm}

\newline

(B)

2.5\,\text{cm}

\newline

(C)

5\,\text{cm}

\newline

(D)

7\,\text{cm}

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Posted 8 months ago

Question

A contractor is to build a new structure at a farm for seed storage. It will have a rectangular base, which is

20

feet wide by

35

feet long, with walls of thickness

t

feet. The structure is

90

feet tall. Excluding the volume of the walls, which of the following functions best models the volume,

V

, in cubic feet, inside the structure?

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Posted 7 months ago

Question

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

\newline

79\%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

\newline

h

, in meters, after

\newline

b

bounces?

\newline

Choose

1

answer:

\newline

(A)

\newline

h=4\cdot0.79^{(b-1)}

\newline

(B)

\newline

h=4\cdot0.79^{b}

\newline

(C)

\newline

h=4-0.79\cdot b^{2}

\newline

(D)

\newline

h=4\cdot(1-0.79\cdot b^{2})

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Posted 8 months ago

Question

Imani's grandmother's house is

5

miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at

10

miles per hour. Which equation best describes the distance,

\newline

d

, in miles, Imani is from home after

\newline

t

hours?

\newline

Choose

1

answer:

\newline

(A)

d=5+10t

\newline

(B)

d=5-10t

\newline

(C)

d=5t+10

\newline

(D)

d=5t-10

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Posted 8 months ago

Question

A piece of wood has a mass of

m_1

grams and a volume of

V_1

cubic centimeters. A second piece of wood has the same density

\rho

and a volume of

V_2

. What is the mass, in grams, of the second piece of wood?

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Posted 8 months ago

Question

The function models

R

, the revenue, in dollars, from selling a particular board game at a price of

x

dollars. What is the revenue if the board game is sold at a price of

30

dollars?

\newline

Choose

1

answer:

\newline

(A)

\$500,000

\newline

(B)

\$800,000

\newline

(C)

\$900,000

\newline

(D)

\$1,770,000

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Posted 8 months ago

Question

Rocio drops a ball from a height of

4

meters. Rocio observes that each time the ball bounces, it reaches a peak height which is

79\%

of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height,

h

, in meters, after

b

bounces?

\newline

Choose

1

answer:

\newline

(A)

h=4\cdot0.79^{(b-1)}

\newline

(B)

h=4\cdot0.79^{b}

\newline

(C)

h=4-0.79\cdot b^{2}

\newline

(D)

h=4\cdot(1-0.79\cdot b^{2})

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Posted 8 months ago

Question

What is the volume, in cubic inches, of a rectangular prism with a height of

7

inches, a width of

5

inches, and a length of

5

inches?

\newline

Answer:

V=\square

inches

^{3}

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Posted 8 months ago

Question

A rectangular prism has a length of

2

inches, a height of

16

inches, and a width of

15

inches. What is its volume, in cubic inches?

\newline

Answer:

V=\square

inches

^{3}

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Posted 8 months ago

View all (116)

A solid consists of a cone, cylinder and hemisphere joined together as shown in the diagram. Given the dimensions indicated in the diagram, find the volume and surface area of the solid, accurate to 333 significant figures.

A solid consists of a cone, cylinder and hemisphere joined together as shown in the diagram. Given the dimensions indicated in the diagram, find the volume and surface area of the solid, accurate to $3$ significant figures.