Draw a cone that is circumscribed about a regular pyramid whose base edge is 5 inches less than 3 times its altitude and whose base central angle π/6 If the base perimeter 18 inches Find the total area , volume of the cone and the pyramid respectively

Q: An aquarium is installing a new fish tank and needs to determine the cost of the glass required to…

A: We have given the  Base side length of the hexagon= 8feet Apothem length= 5feet And, height of the…

Q: A cylinder with a base radius of 6 units and a height of 3 units with a cone of the same base radius…

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Q: Find the area of a regular octagon with side 9. Round to the nearest hundredth if necessary.

A: Area of regular octagon :  A=2(1+√2)*a2 a=9 then A=2(1+√2)*9*9 A=391.1

Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of a Norman…

A: We need to determine the radius of semicircle and height of rectangle.

Q: find the height of a right circular cone with its slant height equal to 16cm and total surface area…

A: Given:- Right circular cone with its slant height equal to 16cm and total surface area is 120 pi…

Q: circle is divided into two parts by a chord, 3 cm away from the center. Find the a of the smaller…

A: Topic:- area of circle

Q: The area of the whole surface of a cone is 64 sq. m. and the slant height is 5 times the radius of…

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Q: Find the area of the largest isosceles triangle that can be inscribed in a circle of radius r=14

A: We will find required as shown below

Q: (a) Decompose this trapezoid into shapes that we know how to find the area of, i.e. triangles,…

A: Given trapezoid:

Q: How far from its center should a grapefruit with a 5-inch diameter be sliced in order that both…

A: We have given

Q: A Norman window consists of a rectangle surmounted by a semicircle. If the perimeter of a Norman…

A: This is a problem of the maxima and minima concepts. For admitting most light into the window its…

Q: 11. Find the dimensions of a rectangle with arca 1000 m whcse perimeter is as small as possible.

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost the other…

Q: A square pyramid has a base with side length 24 cm and has a slant height of 15 cm. What is the…

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Q: Two small circles tangent to each other are inscribed in a rectangle. A bigger circle is…

A: Given, Area of the shaded region = 10 inches2 Let, The diameter of the smaller circles = d The…

Q: A hexagonal prism has a height of 6 units and a regular hexagonal base with a side length of 4…

A: Given:A hexagonal prism has a height of 6 units and a regular hexagonal base with a side length of 4…

Q: A diameter and a chord intersected inside a circle. The point of intersection divides each of the…

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Q: Find the area of the largest isosceles triangle inscribed in a semicircle of radius 10 feet, the…

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Q: The roof of a water tower is composed of 6 equal isosceles triangles whose vertices meet in the…

A: Given that the roof of a water tower is composed of 6 equal isosceles triangles whose vertices meet…

Q: How many liters of paint are needed to paint the exterior wall of an astronomical observatory…

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Q: A regular hexagonal pyramid whose base perimeter is 60 cm has an altitude of 30 cm, the volume of…

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Q: A box-shaped observation terrarium is to be constructed where: the base, left, and right sides of…

A: The sheet of metal starts with the dimensions 8 meters front-to-back by 7 meters left-to-right The…

Q: Surface Area = ______________ Volume =

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Q: Construction workers are digging a tunnel through a mountain like the one below. The space inside…

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Q: Determine the overlapping area in square meter.

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Q: A regular square pyramid has an altitude of 12m and a volume of 196m^3. Determine the slant height…

A: Follow the procedure given below.

Q: A triangular pyramid with an equilateral base has a side length of 10 centimeters and a surface area…

A: Given data: The side of the equilateral triangle base is a=10 cm. The surface area of the triangular…

Q: A wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder…

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Q: 5.A circle whose area is 452 cm2 is cut into two segments by a chord whose distance from the center…

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Q: A right circular cylinder has a radius of 3 units and a volume of 72pie  cubic units. What is the…

A: Topic = Volume

Q: shipping container is in the shape of a right rectangular prism with a length of 2 feet, a width of…

A: Given query is to find the wei of the contents in the container.

Q: What is the height of a right circular cone having a slant height of √(10x) and a base diameter of…

A: A cone is a three-dimensional shape. The slant height of a right circular cone can be calculated…

Q: A rectangle is to be inscribed in a semicircle with radius 5.5, with one side on the semicircle’s…

A:

Q: A margarine tub has the shape of the frustrum of a cone. With the lower base having diameter length…

A: Volume of frustrum of the cone is, V=13πR2H-r2h       ...(1)

Q: A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the…

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Q: The cross-section of a trough is an isosceles trapezoid. If the trough is made by bending up the…

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Q: hemispherical tank of radius 6 feet is positioned so that the base is circular. How much work is…

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Q: 1. Find the total area and volume of frustum of regular square pyramid, whose base have sides 10 cm…

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Q: Find the dimension of the largest cylinder that can be inscribed in a cone of a height 8m and radius…

A: Consider the following figure Let r and h be the radius and height of the inscribed cylinder.…

Q: In a frustum of a cone the radii of the base circles are 35  cm and 9 cm. If the altitude is 2 cm,…

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Q: Two cubes of same side 6 cm are joined end to end. Then, the total surface area of the new cuboid is…

A: Formula Used: Surface area of cuboid   Surface Area=2 [lb+bh+hl]

Q: Find the total surface area (cm2) of the square pyramid if its perpendicular height is 12 cm and its…

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Q: A town park was constructed to form a shape of a trapezoid. The base measures 128meters and 92…

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Q: Two small circles tangent to each other are inscribed in a rectangle. A bigger circle is…

A: Let the radii of the small incscribed circles be r. The area of a circle with a radius r is A=πr2.…

Q: he lateral edge of a regular hexagonal pyramid is two times the length of the base edge. If the…

A: Question is solved.

Q: a) A triangle is inscribed in a semi-circle, its hypotenuse lies on the diameter of the semi-circle.…

A: Given: Let ∆ABC is inscribed in semicircle. The angle inscribed in a semicircle is always a right…

Q: . A circular piece of cardboard with a diameter of 1 m will be made into a conical hat 40 cm high by…

A: Use circumference of surfaces

Q: Two similar pyramids have volumes in a ratio of 27:64.  What is the ratio of their heights? (meaning…

A: Given that two similar pyramids have volumes in a ratio of 27:64

Q: The perimeter of a triangle is 102cm and its area is 431.1554cm2. Find the maximum diameter of a…

A: Given: Area of triangle = 431.1554 cm2 Perimeter of triangle = 102 cm We know that the incircle of a…

Q: A rectangular piece of paper with length 37 cm and width 16 cm has two semicircles cut out of it, as…

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