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What are the values for x and y of a cuboid whose dimensions are x cm by y cm by 4 cm having a volume of 135 cubic cm and a surface area of 163.5 square cm?
Volume = length x width x depth = 4xy cm3 = 135 cm3 [1]
Surface area = 2 x (length x width + length x depth + width x depth)
= 2 x (xy + 4x + 4y) cm2 = 163.5 cm2 [2]
From [1]: 4xy = 135 → y = 135/4x
Substituting in [2]:
2(xy + 4x + 4y) = 163.5
→ 2(x(135/4x) + 4x + 4(135/4x)) = 163.5
→ 135/2 + 8x + 270/x = 327/2
→ -96 + 8x + 270/x = 0
→ 4x2 - 48x + 135 = 0
→ (2x - 15)(2x - 9) = 0
→ x = 7.5 or 4.5
→ y = 4.5 or 7.5 (respectively).
Thus the cuboid is 7.5 cm by 4.5 cm by 4 cm.
What else can I help you with?
What is the similarity between a cuboid and a square based pyramid?
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What is the square feet of 26 feet x 54 feet and 10 inches deep?
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The total surface area of a cuboid with edges of length a, b and c units is 2*(ab + bc + ca) square units.
How do you calculate the dimensions of a square pyramid with a surface area of 350cm2?
There is not enough information to calculate the dimensions.
What 3d shape has the same cross section as a square?
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
Formula of surface area of cuboid?
Let its dimensions be a, b and c:- Surface area of the cuboid: 2*(a*b)+2*(b*c)+2*(a*c) in square units
What is the similarity between a cuboid and a square based pyramid?
Both a cuboid and a square-based pyramid are three-dimensional geometric shapes. They share the characteristic of having a square base, with the cuboid having equal-length edges and right angles, while the pyramid has triangular sides that converge at a single apex. Additionally, both shapes can be defined by their height, and their volume can be calculated using specific formulas related to their dimensions.
Formulas of cuboid?
Following are the formulas of cuboid. Let the dimensions of the cuboid be l (length), w(width) and h (height). Lateral surface area of the cuboid = perimeter of rectangular base x height = 2(l + w)h square units= 2h(l + w) square units; Total surface area (TSA) = 2 (lw + wh + hl); Volume of cuboid (V) = lwh. Length of diagonal of one side is √(l^2 + w^2), √(w^2 + h^2), √(h^2 + l^2) - depending upon side. Length of diagonal across the cuboid is √(l^2 + w^2 + h^2)
Is a square prism a cuboid?
A square prism is always a cuboid.
What is the square feet of 26 feet x 54 feet and 10 inches deep?
There are three measures given but the shape is not specified. I shall assume that it is a cuboid (rectangular prism).The total surface area of the shape is 2941.33... square feet.There are three measures given but the shape is not specified. I shall assume that it is a cuboid (rectangular prism).The total surface area of the shape is 2941.33... square feet.There are three measures given but the shape is not specified. I shall assume that it is a cuboid (rectangular prism).The total surface area of the shape is 2941.33... square feet.There are three measures given but the shape is not specified. I shall assume that it is a cuboid (rectangular prism).The total surface area of the shape is 2941.33... square feet.
What is the formula for finding the area of a cuboid?
The total surface area of a cuboid with edges of length a, b and c units is 2*(ab + bc + ca) square units.
How do you calculate the dimensions of a square pyramid with a surface area of 350cm2?
There is not enough information to calculate the dimensions.
What 3d shape has the same cross section as a square?
The following are some shapes having a square cross section: a cube, a cuboid, a square pyramid.
How many square faces does a cuboid have?
A cuboid can have 2, 4 or 6 square faces.
Surface area of cuboid and cube?
For a cuboid, the total surface area = 2*(L*B + B*H + H*L) square units where L = length, B = breadth and H = height.In the case of a cube, L = B = H and so the total surface area is 6*L^2 square units.
What is the difference between a square and a cuboid?
A square is a 2-dimensional figure, a cuboid is 3-dimensional.
What is the closed surface area of a cuboid?
It is the sum of each of the six square faces. Each face has an area of s2 square units where s is the side length. So the total surface area is 6s2 square units.
