Surface Area Calculation Problems for Solid Shapes.
To calculate the surface area of a solid object:1. Identify the shape (e.g., cube, sphere, cylinder) and use its specific formula.
2. Measure the required dimensions, such as side length (cube), radius (sphere), or height and radius (cylinder).
3. Apply the formula (e.g., 6a2 for a cube, 4πr2 for a sphere).
4. Substitute the values into the formula and perform the calculations.
5. Include units (e.g., cm², m²) in your final answer.
For composite shapes, break them into simpler parts and sum their surface areas.
Number of problems found: 1030
- The height 4
The height and radius of a cylinder are 25 ft and 5 ft, respectively. What is the surface area? - The dimensions
The dimensions of a rectangular piece of paper are 22 cm × 14 cm. It is rolled once across the breadth and once across the length to form right circular cylinders of biggest possible surface area. Find the difference in volumes of the two cylinders that w - New drink
Create a new drink can that will double the volume of the original can used. The dimensions of the can: 6cm diameter and 10cm height. You are to double the volume with the least amount of additional aluminum needed for the new can. There are 3 options : O - Tent - spherical cap
I have a tent in the shape of a spherical cap. Assume we want the volume to be 4 cubic meters, to sleep two or three people. Assume that the material making up the dome of the ten is twice as expensive per square as the material touching the ground. What - Storage shed
Frank designed a net for a storage shed that he is going to construct out of metal. The design consists of a square base and four square sides, plus four triangular parts that make up the roof. A square base of 6 feet and four square sides, plus 4 feet of - Jane and tent
Jane and her father were going to the tent. They found that their old tent was torn. Their mother suggested that they sew a tent whose walls would be made of 4 identical isosceles triangles. Their lower side is 2 m long, and the height is also 2 m. Then, - Cuboid - sum of edges length
Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - A cone 3
A cone has a diameter of x cm and a slant height of y cm. A square pyramid has a base side length of x cm and a slant height of y cm. Which has the greater surface area? Explain. - A bakery
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one-fourth inches in height. If each mini muffin is completely wrapped in paper, how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7. - A lamp
A lamp shade like that of a frustum has a height of 12 cm and an upper and lower diameter of 10 cm and 20 cm. What area of materials is required to cover the curved surface of the frustum? - Saria
Saria is wrapping a gift for her mother. The gift box is in the shape of a rectangular prism and is 5 centimeters high, 25 centimeters long, and 40 centimeters wide. How much wrapping paper will you need to wrap the gift box? - The radius 3 The radius of a solid circular cylinder decreases by 20% and its height increases by 10% . Find the percentage change its : (a) volume (b) curved surface area.
- Two cubes 2 Two cubes each of volume 125 cm³ are joined end to end. Find the surface area of the resulting cuboid .
- Spheres - ratios
The surface area of two spheres are in the ratio 1 : 4 . Find the ratio of their volumes. - A cube 4
A cube of edge 5 cm is cut into cubes, each of edge 1 cm. Find the ratio of the total surface area of one of the small cubes to that of the large cube. - A frustum
A frustum of a pyramid consists of a square base of length 10 cm and a top square of length 7 cm. The height of the frustum is 6 cm. Calculate the surface area and volume. - Eva wraps
Eva wraps a gift box in the shape of a right rectangular prism. The figure shows a net for the gift box. How much wrapping paper did she use, in square meters? - A capsule
A medicine capsule is a cylinder with two hemispheres stuck to each end. Its length is 14 mm, and its diameter is 5 mm. Find its surface area. - The surface 5
The surface area of a cylinder is 6140 cm², and the radius is 25 cm. What is the height? - Surface = volume
If the volume and the surface area of a sphere are numerically the same then find its radius.
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