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mathematics UK Year 10 Mathematics (KS4)

Solved problems for the chapter:

Surface Area of Solids

View the theory »

Prism for KS4

1. Types of prisms

1.1. Vertical and oblique prisms

1.2. Regular prisms

1.3. Equilateral prism

2. Prism surface area

3. Prism volume

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:surface_area_of_solids/3667/

Example 1.

Circle the correct answers. The base area of a cuboid can be:

triangle
square
rectangle
rhombus

Example 2.

The length of all the sides of a cuboid is 96 cm. Calculate the length of a cuboid if it is 8 cm wide and 6 cm high .

The base area of a cuboid is . Calculate the total surface area of the cuboid if its lateral surface area is .

Calculate the diagonal of the base surface of a cuboid whose base is 15 cm long and 8 cm wide. Use the Pythagorean theorem.

A cuboid is sketched above, Using pythagorean theorem, write the formula for calculating the lateral face diagonal of the cuboid , also, use the formula to express the height of the cuboid .

The cuboid above is 15 cm long, 6 cm wide and 8 cm high. Calculate the area of the marked cross section of the cuboid.

Using Pythagorean theorem, write a formula for calculating the diagonal .

From this formula, express the length of the cuboid.

A cuboid is sketch below.

Write down the formula by which we use the Pythagorean theorem to calculate the space diagonal of a cuboid, and from it express the diagonal of the base plane as the subject of the formula.
Write a formula with which we use the Pythagorean theorem to calculate the space diagonal of a cuboid, using the length a, the width b and the height c and express the width b of the cuboid as the subject of the formula.

Cube and cuboid have equal volume . At the same time, the edge of the cube is the same length as the width of the cuboid. Calculate the total surface area of the cube and the cuboid if the length of the cuboid is 12.8 cm.

10.

When playing billiards, players first arrange the balls inside a triangular frame (equilateral triangle). Calculate the radius of each sphere to 2 significant figures if the height of the triangular frame is and the balls are arranged.

11.

The surfaces area of a sphere and an equilateral cone are in the ratio . Calculate the ratio of their volumes.

12.

We have a given cone with radius and height . Calculate its volume and total surface area.

13.

The diagonal of a cube measures . Calculate the surface area and volume of the cube.

14.

The area of the squares of a cube measures . Calculate the surface area and volume of the cube.

15.

Draw the development of the figure below where side length of the cube is 4 cm.

Figure

16.

Calculate the surface area and volume of a cube with height .

17.

The diagonal of the square which form a cube measures . Calculate the surface area and volume of the cube.

18.

Calculate the surface area of a cube whose volume measures .

19.

Calculate the area of the right circular cylinder given it's radius and it's volume, .

20.

In a right circular cylinder, the area of the base plane and the curved surface area measured . Calculate the total surface area and volume of the cylinder.

21.

Calculate the surface area of a cube whose side measures 4.87 cm. What will be the length of the side of the cube if its surface area is increased by 43%?

22.

A triangular prism with base area and triangular surface areas of , and is to be cut out from a paper. Calculate the paper needed in .

23.

The sum of all the lengths of the sides of a cuboid is . Calculate the area and volume of this cuboid if the lengths of the sides are in the ratio a: b: c = 6: 2: 5.

24.

The volume of a cuboid measures , and its sides are in the ratio a: b: h = 10: 3: 5. Calculate its surface area.

25.

Calculate the area of all diagonal sections of a cuboid whose length is 5 times and height 3 times of width measuring 7 cm.

26.

Calculate the surface area and volume of an equilateral triangular prism with side a = 5 cm.

27.

Calculate the ratio of the surface areas and volumes of a regular triangular and a regular hexagonal prism that are 6.7 cm high and their base side measures 3.9 cm.

28.

Calculate the surface area and volume of an equilateral prism with side a = 4 cm.

29.

Mom bought a vase in the shape of an equilateral triangular prism. She poured 1.3 liters of water and the vase was filled to . Calculate the surface area of this vase.

30.

A circle is inscribed to the base of a equilateral triangular prism. If its radius measures 4 cm, calculate the surface area and volume of the prism when it is 10 cm high.

31.

Calculate the angle between the body diagonal of the cube and the side CG of the cube as shown in the figure below.

Figure

32.

Calculate the surface area and volume of a regular octagonal prism with base side a = 4 cm and 10 cm high.

33.

The sketch above shows the axial section of a right-angled circular cylinder. Calculate the area of this cylinder.

34.

A trapezium with sides a = 17 cm, b = 12 cm, c = 8 cm and d = 11 cm is the base of a four-sided prism having a height equal to one third of the base perimeter. Calculate the surface area and volume of the prism.

35.

A trapezium with sides a = 17 mm, b = d = 12 mm and c = 8 mm is the base of a four-sided prism whose rectangular surface area is equal to the base area. Calculate the surface area and volume of the prism.

36.

Given a regular square prism with base edge a = 10 cm and height h = 15 cm. Calculate the total surface area and volume of the hollow cylinder bounded by a prism delineated and inscribed cylinder.