SURFACE AREA AND VOLUME OF RECTANGULAR PRISM WORD PROBLEMS WORKSHEET

Problem 1:

The lateral surface area of a cuboid whose length, width  and height are 2a, 2b and 2c respectively is

a)  2(ab + bc + ca)    b)  4(ab + bc + ca)

c)  8(a + b) c     d)  none of these

Solution

Problem 2 :

The sum of the areas of all faces (excluding top and bottom) of a cuboid is the ___________ of the cuboid.

a) Volume      b) lateral surface area

c) Total surface area     d) none of these

Solution

Problem 3 :

The volume of a cuboid whose length, breadth and height are 2a, 3a and 4a is

a)  24a²    b)  24a³     c) 12a³     d) none of these

Solution

Problem 4 :

Find the height of a cuboid whose volume is 756 cm³ and base area is 63 cm²?

Solution

Problem 5 :

The dimension of a cuboid are in the ratio of 2:3:4 and its total surface area is 280 m². Find the dimensions.

Solution

Problem 6 :

A cuboid is 40 cm × 20 cm × 10 cm. what would be the side of a cube having the same volume?

a) 20 cm     b) 40 cm    c) 10 cm    d) 30 cm

Solution

Problem 7 :

A cuboid has a volume of 3000 cm³, with height 15 cm and length 20 cm. Find the area of the upper surface.

Solution

Problem 8 :

The sum of length, breadth and depth of a cuboid is 19 cm and the diagonal is 5√5. Find its surface area.

Solution

Problem 9 :

Three cubes with sides in the ratio 3:4:5 are melted to form a single cube whose diagonal is 12√3 cm. find the sides of the cube.

Solution

Problem 10 :

A company is designing a juice box. The box is in the shape of a rectangular prism. The base of the box is 6 1/2 inches by 2 1/2 inches, and the box is 4 inches high. If juice fills 90% of the box’s volume, find the volume of juice in the box.

Solution

Problem 1 :

The bottom of a tank measures 50 m × 40 m. Find its depth if it contains 4000 m³ of water.

Solution

Problem 2 :

The volume of a rectangular prism whose length, breadth and height are 2a, 3a and 4a is.

a) 24a²        b) 24a³        c) 12a³      d) none of these

Solution

Problem 3 :

The surface area of a cuboid is 1372 sq. cm. If its dimensions are in the ratio of 4 : 2 : 1, find the volume.

Solution

Problem 4 :

The volume of a rectangular prism is 24 ft³, the height is 2, what are three possible measures for the length and width of the prism?

Solution

Problem 5 :

A box of tissues has a length of 11.2 cm, a width of 11.2 cm and a height of 13 cm. What is the volume of the tissue box ?

Solution

Problem 6 :

A terrarium is shaped like a rectangular prism. The prism is 25 1/2 inches long, 13 1 / 2 inches wide, and 16 inches deep. What is the volume of the terrarium?

Solution

Problem 7 :

A block of wood measures 4.5 inches by 3.5 inches by 7 inches. What is the volume of the block of wood?

Solution

Problem 8 :

A restaurant buys a freezer in the shape of a rectangular prism. The dimensions of the freezer are shown. What is the volume of the freezer?

Solution

Problem 9 :

Rectangular prism A measures 6 inches by 4 inches by 5 inches. Rectangular prism B’s dimensions are twice those of prism A. Find the volume of each prism. How many times as great is prism B’s volume as prism A’s volume?

Solution

Problem 10 :

Leticia has a small paper weight in the shape of a rectangular prism. The dimensions of the paper weight are shown. What is the volume of the paper weight?

Solution

Problem 11 :

The dimensions of a rectangular prism are 3 1/4 feet by 2 1/2 feet by 5 feet.

• Lee found the volume by multiplying 12 1/2 by 3 1/4
• Lola found the volume by multiplying 16 1/4 by 2 1/2

Who is correct? Explain.

Solution

Find the 

(i) Lateral surface area and 

(ii)  Total surface area of the following rectangular prism.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 : 

Solution

Problem 6 : 

A rectangular room is 12 feet by 21 feet. The walls are 8 feet tall. Paint is sold in one gallon containers. If a gallon of paint covers 450 sqaure feet, how many gallons of paint should poloma buy to paint the walls of the room ?

Solution

Problem 7 : 

The scale factor of prism X to prism Y is 2/3. What is the ratio of the surface area of prism X to the surface area of prism Y.

Solution

Problem 8 : 

The greater the surface area of an ice block, the faster it will melt. Which will melt faster, the bigger block or the three smaller blocks? Explain your reasoning.

Solution