Each face of a cube has an area of 64\text{ cm}^{2}.
Find the length of the cube's edge.
Find the volume of the cube.
Find the side length of a cube that has a surface area of 600\text{ cm}^2.
The curved area of a cone is 380\text{ cm}^{2} and the slant height is 15\text{ cm}:
Find the radius of the cone, correct to two decimal places.
Find the perpendicular height of the cone, correct to one decimal place.
Find the total surface area of the cone, correct to the nearest whole number.
Find the height, h, of this closed cylinder if its surface area is 27\,288\text{ mm}^{2} and its radius is 43\text{ mm}.
Round your answer to the nearest whole number.
A square pyramid has a surface area of 310\text{ cm}^{2}, and the area of its square base is 25\text{ cm}^2.
Find the area of each triangular face.
Find the height of each triangular face.
Find the perpendicular height of the pyramid correct to one decimal place.
A cone has a surface area of 560\text{ cm}^{2} and a radius of 6\text{ cm}.
Find the slant height of the cone. Round your answer to two decimal places.
Find the perpendicular height of the cone. Round your answer to one decimal place.
A sphere has a surface area of 450\text{ cm}^{2}. Find its radius correct to two decimal places.
A ball has a surface area of 50.27\text{ mm}^2. Find its radius to two decimal places.
A ball has a surface area of 1809.56\text{ m}^2.
Find its radius to the nearest metre.
Find the volume of the ball to two decimal places.
The following rectangular prism has a volume of 168\text{ mm}^3:
Find the length, a, of the rectangular prism.
The following rectangular prism has a volume of 1680\text{ mm}^3:
Find the width of the rectangular prism in millimetres:
Find the side length of a cube with volume 27\text{ cm}^3.
Find the length of the rectangular prism with volume 162\text{ cm}^3, width 6\text{ cm} and height 3\text{ cm}.
The volume of the triangular prism shown is 231\text{ cm}^3.
Find the value of k.
The volume of the triangular prism shown is 287.5\text{ m}^{3}.
Find the value of k, to one decimal place.
The volume of the triangular prism shown is 247.45\text{ cm}^{3}.
Find the value of y to one decimal place.
A pentagonal prism has a volume of 176.4\text{ m}^3 and a cross sectional area of 29.4\text{ m}^2. Find the height of the prism.
Find the cross-sectional area of a pentagonal prism, if the volume is 470\text{ mm}^3 and the height is 10\text{ mm}.
A square pyramid has a base with side length 12\text{ mm} and a volume of 1248\text{ mm}^3. Find the height of the prism.
A rectangular pyramid has a volume of 432\text{ cm}^{3}. The height of the pyramid is 18\text{ cm} and the width of the base is 6\text{ cm}. Find the length of the base.
A rectangular pyramid has a volume of 288\text{ cm}^3. The base has a width of 12\text{ cm} and length 6\text{ cm}. Find the height of the pyramid.
A square pyramid has a height of 24\text{ cm} and a volume 2592\text{ cm}^3. Find the base side length of the pyramid.
A cone has a volume of 26\,640.97\text{ cm}^3 and radius 31.9\text{ cm}. Find the height of the cone. Round your answer to the nearest centimetre.
A cone has a volume of 1273.39\text{ mm}^{3} and height 19\text{ mm}. Find the radius of the cone to the nearest millimetre.
A cone has a volume of 196\text{ mm}^3. If the height and radius of the cone are equal in length, find the radius of the cone. Round your answer to two decimal places.
A sphere has a radius of r\text{ cm} and a volume of \dfrac{343 \pi}{3}\text{ cm}^3. Find the radius of the sphere to two decimal places.
If the volume of a sphere is 20\,579.526\text{ cm}^3, find the length of its diameter. Round your answer to one decimal place.
A hemispherical bowl has a capacity of 2.5\text{ L}. Find its radius in centimetres. Round your answer to one decimal place.
A cylindrical water tank has capacity 90\,000\text{ L} and a height of 2.5\text{ m}. Find the length of its diameter. Round your answer to one decimal place.
This nesting box needs to have a volume of 129\,978\text{ cm}^{3}, a height of 83\text{ cm} and a width of 54\text{ cm}.
Find the depth, d, of the box.
The volume of the following tent is 4.64\text{ m}^3.
Find the height, h, of the tent.
A swimming pool has the shape of a trapezoidal prism as shown in the diagram.
Find the volume of the pool.
If the pool is only three-quarters full, find the volume of the empty space in the pool.
If the distance from the water level to the top of the pool is h\text{ m} when it is is three-quarters full, find the value of h.
A cylindrical paddle-pool with radius 1.4\text{ m} has a water depth of 47\text{ cm}.
Find the volume of water in the pool, in cubic metres. Round your answer to three decimal places.
If 100\text{ L} of water is added, by how many centimetres does the depth of the water increase? Round your answer to one decimal place.
A spherical steel shot-put has a mass of 5.3\text{ kg}. Given that the density of the steel used is 8070\text{ kg/m}^3, find:
The volume of the shot-put in cubic centimetres. Round your answer to one decimal place.
The radius of the shot-put in centimetres. Round your answer to one decimal place.
Yuri has 6\text{ m}^2 of metal sheeting out of which he plans to make a raised garden bed. He is considering two designs:
Design 1: An open rectangular prism with height 0.4\text{ m}, and two sides 4.2\text{ m} long (no top or base), or
Design 2: An open cylinder with height 0.4\text{ m} (no top or base)
Find the length, l, of the other two sides of the rectangular design. Round your answer to two decimal places.
Find the radius, r, of the cylindrical design.
Which design will give the larger volume for the garden bed?
