The sum of the lengths of all edges of a cube is 60 cm. Find the volume V and the surface area T of the cube.

Q: The base of a prism is a hexagon inscribed in a circle. If the difference in the circumference of…

A: Let's find.

Q: A triangular sandpit having side lengths 5 m, 4 m and 8 m is to be constructed to a depth of 20 cm.…

A: The volume of a solid is calculated by multiplying the area of the base by the height/depth. The…

Q: Find the radius of a cone if it has a volume of 960r in', and a height of 20 in. V= 1 - Tr²h 3

A: We have to find the radius

Q: What is the edge length of a cube with a volume of 1 L?

A: Volume of a cube is 1 L.

Q: The volume of a cylinder is 72 m and the radius is 3 m. What is the height of cylinder?

A: GivenVolume of the cylinder = 72 m^3and Radius of the cylinder = 3 m

Q: Given a cylinder with a base area of 144π in² and the height that is twice the radius. Find the…

A: The lateral surface of an object is the area of all the faces of the object, excluding the area of…

Q: Find the volume of the Sphere 5 m¸-

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Q: The base of the pyramid is 72 cm, and the length of TP = 15 cm. The volume of the pyramid is..

A: Let B be a base B=72cmLet h be a length of TP h=15cmVolume of pyramid =13Bh=13×72×15=360 cm3

Q: The numerical value of the volume of a cube equals the numerical value of its total surface area.…

A: Given, The volume of a cube=The surface area of cube To find the length of each edge of the cube.

Q: A box with a square base has length plus girth of 108 in. (Girth is the distance "around" the box.)…

A: Consider the diagram, Observe that the box with a square base has length plus girth of 108 in. Here…

Q: Give the dimensions of a box with 5 sides that has a surface area of 300 cm? and holds the largest…

A: Let the dimension of the box is l×b×h, so the surface area of five-sided box is: S=2lb+2bh+lh Given,…

Q: If the length of one side of a cube is 4 m. Find its Volume.

A: A Cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges in…

Q: 4. The altitude of a right hexagonal prism is twice as long as the edge of the base. If the prism…

A: Given Volume = 1923in3

Q: the volume of a sphere whose radius is 2cm is four times that of a sphere whose radius is 1cm true…

A: Given,         The volume of a sphere whose radius is 2 cm is four times that of a sphere whose…

Q: Find the volume of a pyramid whose base is a square with side L and whose height is H

A: Pyramid: base is a square with side L. base area = L x L = L2 height = H…

Q: The bases of a right prism is a hexagon with one of each side equal to 6 cm. The bases are 12 cm…

A:

Q: If the length of the side of a cube is 3x, what is the volume of the cube? What is the surface area…

A: Given,           The length of the side of a cube is 3x.To find : What is the volume of the cube?…

Q: Find the dimensions of the rectangular box with the largest volume if the total surface area given…

A: It is known that the surfaces area for the rectangular box with edges is x,y and z is 2xy+yz+zx and…

Q: The altitude of a regular square pyramid is 4 cm. If the volume is 48 cm. Find the total area of the…

A: The altitude of the regular square pyramid  h = 4 cm Volume of pyramid V = 48 cm3

Q: If 1200 cm? of material is available to make a box with a square base and an open top, find the…

A: Given, material available = 1200 cm2 Let's assume the sides of the square base = a Height of the…

Q: A cylinder has a height of 12 in. and a radius of 4 in. How can you change the radius of the…

A: Given the height of a cylinder h=12inch and radius of the cylinder r=4inch We need to find the…

Q: The base of a right prism is a rhombus one side of which is 10 cm, and the shorter diagonal is 12…

A: We will find the volume of the right angle prism in the following step.

Q: Find the dimensions of a rectangular prism whose volume is (x4 ‒  y4) units3.

A: Given that,                volume, v =  (x4 ‒  y4) units3

Q: Cone A has a radius 12 inches and Cone B has a radius of 30 inches. If the cones are similar and the…

A:

Q: If a cube has a surface area of 216 cm2, what is its volume?

A:

Q: Find the volume of a regular triangular pyramid if the length of one side of the base is 12 cm and…

A:

Q: 2) Find the radius of a cylinder with a volume of 339.1 in' and a height of 12 in.

A: Volume of cylinder is πr2h. Use this formula to find the value of radius of cylinder.

Q: Find the volume of a pyramid with a square base with a perimeter of the base is 12.8m and the height…

A:

Q: In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If…

A: Given that, the sum of the external and internal radii is 14 cm and the width is 4 cm. The height of…

Q: If the radius length of one sphere is three times as long as the radius length of another sphere,…

A: Let a be the length of the radius of the smaller sphere.Since, it is given that the length of one…

Q: Find the radius and volume of this cylinder with a height of 10 and a surface area of 78π.

A:

Q: When the radius of a sphere is doubled, the volume of the new sphere is as large as the volume of…

A: The new radius is 2r now, So, the new volume will be: V=43π(2r)3=43π(8r3)=843πr3=8(old volume)

Q: The volume of the sphere is 36 π cm3.Find the surface area of the sphere ,correct to the nearest

A:

Q: If 1200 cm² of material is available to make a box with a square base and an open top, hnd the…

A: Total area is given so first let the base length is a and height is h .. then make the relation of…

Q: A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of…

A: A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of…

Q: Find the height and radius of a cylinder with volume 250pi in^3 and with the smallest total surface…

A: The volume of the cylinder with radius r and height h is V = 250π in3  ⇒ πr2h = 250π…

Q: A prism has a volume of 213 ft3. what is the volume of a pyramid that has the same base and height…

A:

Q: The dimensions of a pasta box are 14in by 1.5 in by 3 in. what is the surface area of the box?

A:

Q: Find the edge of a cube whose volume is equal to that of a rectangular bar measuring 126 cm long, 4…

A:

Q: has dimensions of 9 in., 10 in., and I ft. 21. Find the volume and the surface area of a "closed…

A: Solution Formula Volume =(length × breadth × height) Surface area =2(lb+lh+hb)

Q: The volume V of the right circular cone is . If the height is twice the radius, which of the…

A:

Q: Find the volume of a rectangular solid whose dimensions are in the ratio 4:6:8 if the radius of the…

A: We need to find the volume of a rectangular solid whose dimensions are in the ratio 4:6:8 if the…

Q: The volume of a sphere is 36π m 3 .Find its area?

A: Given:Volume of a sphere=36 π m3Formula:Surface area of sphere=4 π r2Volume of sphere=43πr3

Q: The edge of a regular dodecahedron is 6 m, what is its total surface area?

A: Given:  The edge of a regular dodecahedron is 6 m. To Find: Total surface area of the given regular…

Q: what would the volume of a sphere with a radius of 12 feet be

A: Volume of sphere having radius 'r' is given as; V=(4/3)πr3.

Q: Multivariable optimization question

A:

Q: A regular square pyramid has lateral area of 60m^2 and base edge of 6m. What is its volume?

A: Given that, A regular square pyramid has lateral area of 60 m2 and base edge of 6 m. We have to find…

Q: The volumes of two similar solids are 729 m3 and 125 m³. The surface area of the larger solid is 324…

A:

Q: ron whose edge measures 6 m

A: Given that the edge measure of a regular icosahedron is 6m.