Find the surface area of the following solids:
Consider the following shape with both boxes that are identical in size:
Find the surface area of both boxes if they had all faces exposed.
Find the surface area of the two circular faces of the cylinder. Round your answer to two decimal places.
Find the area of the curved face of the cylinder. Round your answer to two decimal places.
Hence, find the surface area of the solid.
Find the surface area of the following solids, rounding your answers to two decimal places where necessary:
Find the total surface area of the solid shown, correct to the nearest \text{cm}^2.
For each of the following cylinders:
Find the external surface area of the curved surface to two decimal places.
Find the total surface area of the front and back rings to two decimal places.
Find the internal surface area of the curved surface to two decimal places.
Hence, find the total surface area of the solid to two decimal places.
Consider the following solid hemisphere:
Find the area of the curved surface of the dome. Round your answer to three decimal places.
Find the area of the circular base of the hemisphere. Round your answer to three decimal places.
Hence, find the total surface area of the hemisphere. Round your answer to three decimal places.
Find the total surface area of the following hemispheres. Round your answer to three decimal places.
A hole of diameter 3 cm has been drilled through the centre of a solid cube of side length 7 cm. The resulting solid is to be painted to protect it from rust. Find the total surface area of the solid to be painted correct to the nearest \text{ cm}^2
The given diagram shows the design for a marquee (tent). The roof of the marquee has a height of 3\text{ m}. The material for the marquee costs \$44/\text{m}^{2}.
Find the total surface area of the marquee. Do NOT include the floor.
Find the total cost of the marquee material.
Xavier has been hired to wallpaper the walls and ceiling of a living room. The room is 9.7\text{ m} long, 4.2\text{ m} wide, and 2.91\text{ m} high. There is one window that is 2.3\text{ m} by 1.1\text{ m}, two windows that are 0.97\text{ m} by 1.1\text{ m}, and two doors that are 1.34\text{ m} by 2.6\text{ m}.
Xavier needs to wallpaper everything except the floor, the windows, and the doors. Find the total surface area that Xavier needs to wallpaper, rounding your answer to two decimal places.
A steel shed is to be constructed, with dimensions as shown below. The shed is to include a rectangular cut-out at the front for the entrance.
Determine the surface area of the shed. Round your answer to one decimal place.
Construction of the shed requires an additional 0.1\text{ m}^2 of sheet metal for each 1\text{ m}^2 of surface area, due to overlaps and wastage.
How much sheet metal is required to construct this shed? Round your answer up to the nearest square metre.
If the steel sheets cost \$18 per square metre, calculate the total cost of the steel required to build this shed.
The lid of this treasure chest is found to be exactly one half of a cylindrical barrel. Find the surface area of the chest, correct to two decimal places.
The diagram shows a water trough in the shape of a half cylinder:
Find the surface area of the outside of this water trough. Round your answer to two decimal places.
A grain silo is built with the dimensions as shown:
Find the curved surface area of the exterior of the grain silo. Give your answer in square metres to three decimal places.
Find the curved surface area of the interior of the grain silo. Give your answer in square metres to three decimal places.
How much larger is the exterior curved surface area compared to the interior curved surface area? Round your answer as a percentage to two decimal places.
A wedding cake consists of three cylinders stacked on top of each other. The dimensions are as follows:
- The top layer has a radius and height of 20\text{ cm}.
- The middle layer has the same height as the top layer and a radius that is double that of the top layer.
- The bottom layer has a height that is double that of the top layer, and a radius that is triple that of the top layer.
All the sides and top surfaces are to be covered in icing, but not the base. Find the surface area of the cake that needs to be iced. Round your answer to the nearest square centimetre.
A company manufactures nuts shaped like regular hexagonal prisms, with cylindrical bolt holes cut out of the centre, as shown below:
The total surface area of a nut before the bolt hole is drilled is 14.7\text{ cm}^2. Find the surface area of a single nut after the bolt hole is drilled out, including the inside surface area of the hole. Round your answer to one decimal place.
Each nut that is manufactured requires a zinc coating to prevent corrosion. If 1 \text{ kg} of zinc is enough to coat a surface area of 1\text{ m}^2, how many nuts can be coated with 1 \text{ kg} of zinc? Round your answer to the nearest whole number.
The following concrete water main requires a protective coating before it can be used:
Find the curved surface area of the exterior of the water main. Round your answer to two decimal places.
If the water main needs a protective coating on it's exterior and it costs \$0.12/\text{m}^2. Calculate the cost to coat the pipe.
The following culvert will be part of a water main:
The diameter of the inside of the culvert is 2\text{ m} more than 4 times the thickness of the culvert, x. The length of the tube is 8 times the thickness of the culvert, x.
Write an expression for the interior radius in terms of x.
Write an expression for the exterior radius in terms of x.
Find the exact curved surface area of the interior of the culvert in terms of x.
Find the exact curved surface area of the exterior of the culvert in terms of x.
Find the difference between the interior and exterior curved surface areas in terms of x.
If the thickness of the culvert is 0.5 \text{ m}, find the difference between the interior and exterior curved surface areas. Round your answer to two decimal places.